gap> f[1]:=(1,2,3,4,5); Error, Variable: 'f' must have a value gap> f[2]:=(1,6,7,8,2); Error, Variable: 'f' must have a value gap> f[3]:=(2,8,9,10,3); Error, Variable: 'f' must have a value gap> f[4]:=(3,10,11,12,4); Error, Variable: 'f' must have a value gap> f[5]:=(5,4,12,13,14); Error, Variable: 'f' must have a value gap> f[6]:=(1,5,14,15,6); Error, Variable: 'f' must have a value gap> f[7]:=(16,20,7,6,15); Error, Variable: 'f' must have a value gap> f[8]:=(7,20,19,9,8); Error, Variable: 'f' must have a value gap> f[9]:=(11,10,9,17,18); Error, Variable: 'f' must have a value gap> f[10]:=(12,11,18,17,13); Error, Variable: 'f' must have a value gap> f[11]:=(15,14,13,17,16); Error, Variable: 'f' must have a value gap> f[12]:=(16,17,18,19,20); Error, Variable: 'f' must have a value gap> f:=[1,1,1,1,1,1,1,1,1,1,1,1]; [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] gap> Length(f); 12 gap> f[1]:=(1,2,3,4,5); (1,2,3,4,5) gap> f[2]:=(1,6,7,8,2); (1,6,7,8,2) gap> f[3]:=(2,8,9,10,3); ( 2, 8, 9,10, 3) gap> f[4]:=(3,10,11,12,4); ( 3,10,11,12, 4) gap> f[5]:=(5,4,12,13,14); ( 4,12,13,14, 5) gap> f[6]:=(1,5,14,15,6); ( 1, 5,14,15, 6) gap> f[7]:=(16,20,7,6,15); ( 6,15,16,20, 7) gap> f[8]:=(7,20,19,9,8); ( 7,20,19, 9, 8) gap> f[9]:=(11,10,9,17,18); ( 9,17,18,11,10) gap> f[10]:=(12,11,18,17,13); (11,18,17,13,12) gap> f[11]:=(15,14,13,17,16); (13,17,16,15,14) gap> f[12]:=(16,17,18,19,20); (16,17,18,19,20) gap> f; [ (1,2,3,4,5), (1,6,7,8,2), ( 2, 8, 9,10, 3), ( 3,10,11,12, 4), ( 4,12,13,14, 5), ( 1, 5,14,15, 6), ( 6,15,16,20, 7), ( 7,20,19, 9, 8), ( 9,17,18,11,10), (11,18,17,13,12), (13,17,16,15,14), (16,17,18,19,20) ] gap> for i in [1..12] do > for j in [1..12] do > c[i,j]:=f[i]*f[j]^-1; Syntax error: ] expected c[i,j]:=f[i]*f[j]^-1; ^ > od; > od; gap> for i in [1..12] do > for j in [1..12] do > c.i.j:=f[i]*f[j]^-1; > od; > od; Error, Variable: 'c' must have a value gap> c:=[1]; [ 1 ] gap> gap> for i in [1..12] do > for j in [1..12] do > c[12*(i-1)+j]:=f[i]*f[j]^-1; > od; > od; gap> c; [ (), (1,8,7,6)(2,3,4,5), ( 1, 3, 4, 5)( 2,10, 9, 8), ( 1, 2, 4, 5)( 3,12,11,10), ( 1, 2, 3, 5)( 4,14,13,12), ( 1, 2, 3, 4)( 5, 6,15,14), ( 1, 2, 3, 4, 5)( 6, 7,20,16,15), ( 1, 2, 3, 4, 5)( 7, 8, 9,19,20), ( 1, 2, 3, 4, 5)( 9,10,11,18,17), ( 1, 2, 3, 4, 5)(11,12,13,17,18), ( 1, 2, 3, 4, 5)(13,14,15,16,17), ( 1, 2, 3, 4, 5)(16,20,19,18,17), (1,6,7,8)(2,5,4,3), (), ( 1, 6, 7, 2)( 3,10, 9, 8), ( 1, 6, 7, 8, 2)( 3, 4,12,11,10), ( 1, 6, 7, 8, 2)( 4, 5,14,13,12), ( 1,15,14, 5)( 2, 6, 7, 8), ( 1, 7, 8, 2)( 6,20,16,15), ( 1, 6, 8, 2)( 7, 9,19,20), ( 1, 6, 7, 8, 2)( 9,10,11,18,17), ( 1, 6, 7, 8, 2)(11,12,13,17,18), ( 1, 6, 7, 8, 2)(13,14,15,16,17), ( 1, 6, 7, 8, 2)(16,20,19,18,17), ( 1, 5, 4, 3)( 2, 8, 9,10), ( 1, 2, 7, 6)( 3, 8, 9,10), (), ( 2, 8, 9, 3)( 4,12,11,10), ( 2, 8, 9,10, 3)( 4, 5,14,13,12), ( 1, 6,15,14, 5)( 2, 8, 9,10, 3), ( 2, 8, 9,10, 3)( 6, 7,20,16,15), ( 2, 9,10, 3)( 7, 8,19,20), ( 2, 8,10, 3)( 9,11,18,17), ( 2, 8, 9,10, 3)(11,12,13,17,18), ( 2, 8, 9,10, 3)(13,14,15,16,17), ( 2, 8, 9,10, 3)(16,20,19,18,17), ( 1, 5, 4, 2)( 3,10,11,12), ( 1, 2, 8, 7, 6)( 3,10,11,12, 4), ( 2, 3, 9, 8)( 4,10,11,12), (), ( 3,10,11, 4)( 5,14,13,12), ( 1, 6,15,14, 5)( 3,10,11,12, 4), ( 3,10,11,12, 4)( 6, 7,20,16,15), ( 3,10,11,12, 4)( 7, 8, 9,19,20), ( 3,11,12, 4)( 9,10,18,17), ( 3,10,12, 4)(11,13,17,18), ( 3,10,11,12, 4)(13,14,15,16,17), ( 3,10,11,12, 4)(16,20,19,18,17), ( 1, 5, 3, 2)( 4,12,13,14), ( 1, 2, 8, 7, 6)( 4,12,13,14, 5), ( 2, 3,10, 9, 8)( 4,12,13,14, 5), ( 3, 4,11,10)( 5,12,13,14), (), ( 1, 6,15,14)( 4,12,13, 5), ( 4,12,13,14, 5)( 6, 7,20,16,15), ( 4,12,13,14, 5)( 7, 8, 9,19,20), ( 4,12,13,14, 5)( 9,10,11,18,17), ( 4,13,14, 5)(11,12,17,18), ( 4,12,14, 5)(13,15,16,17), ( 4,12,13,14, 5)(16,20,19,18,17), ( 1, 4, 3, 2)( 5,14,15, 6), ( 1, 5,14,15)( 2, 8, 7, 6), ( 1, 5,14,15, 6)( 2, 3,10, 9, 8), ( 1, 5,14,15, 6)( 3, 4,12,11,10), ( 1,14,15, 6)( 4, 5,13,12), (), ( 1, 5,14, 6)( 7,20,16,15), ( 1, 5,14,15, 6)( 7, 8, 9,19,20), ( 1, 5,14,15, 6)( 9,10,11,18,17), ( 1, 5,14,15, 6)(11,12,13,17,18), ( 1, 5,15, 6)(13,14,16,17), ( 1, 5,14,15, 6)(16,20,19,18,17), ( 1, 5, 4, 3, 2)( 6,15,16,20, 7), ( 1, 2, 8, 7)( 6,15,16,20), ( 2, 3,10, 9, 8)( 6,15,16,20, 7), ( 3, 4,12,11,10)( 6,15,16,20, 7), ( 4, 5,14,13,12)( 6,15,16,20, 7), ( 1, 6,14, 5)( 7,15,16,20), (), ( 6,15,16, 7)( 8, 9,19,20), ( 6,15,16,20, 7)( 9,10,11,18,17), ( 6,15,16,20, 7)(11,12,13,17,18), ( 6,16,20, 7)(13,14,15,17), ( 6,15,20, 7)(16,19,18,17), ( 1, 5, 4, 3, 2)( 7,20,19, 9, 8), ( 1, 2, 8, 6)( 7,20,19, 9), ( 2, 3,10, 9)( 7,20,19, 8), ( 3, 4,12,11,10)( 7,20,19, 9, 8), ( 4, 5,14,13,12)( 7,20,19, 9, 8), ( 1, 6,15,14, 5)( 7,20,19, 9, 8), ( 6, 7,16,15)( 8,20,19, 9), (), ( 7,20,19,10,11,18,17, 9, 8), ( 7,20,19, 9, 8)(11,12,13,17,18), ( 7,20,19, 9, 8)(13,14,15,16,17), ( 7,19, 9, 8)(16,20,18,17), ( 1, 5, 4, 3, 2)( 9,17,18,11,10), ( 1, 2, 8, 7, 6)( 9,17,18,11,10), ( 2, 3,10, 8)( 9,17,18,11), ( 3, 4,12,11)( 9,17,18,10), ( 4, 5,14,13,12)( 9,17,18,11,10), ( 1, 6,15,14, 5)( 9,17,18,11,10), ( 6, 7,20,16,15)( 9,17,18,11,10), ( 7, 8, 9,17,18,11,10,19,20), (), ( 9,18,12,13,17,11,10), ( 9,13,14,15,16,17,18,11,10), ( 9,16,20,19,18,11,10), ( 1, 5, 4, 3, 2)(11,18,17,13,12), ( 1, 2, 8, 7, 6)(11,18,17,13,12), ( 2, 3,10, 9, 8)(11,18,17,13,12), ( 3, 4,12,10)(11,18,17,13), ( 4, 5,14,13)(11,18,17,12), ( 1, 6,15,14, 5)(11,18,17,13,12), ( 6, 7,20,16,15)(11,18,17,13,12), ( 7, 8, 9,19,20)(11,18,17,13,12), ( 9,10,11,17,13,12,18), (), (11,18,13,12)(14,15,16,17), (11,17,13,12)(16,20,19,18), ( 1, 5, 4, 3, 2)(13,17,16,15,14), ( 1, 2, 8, 7, 6)(13,17,16,15,14), ( 2, 3,10, 9, 8)(13,17,16,15,14), ( 3, 4,12,11,10)(13,17,16,15,14), ( 4, 5,14,12)(13,17,16,15), ( 1, 6,15, 5)(13,17,16,14), ( 6, 7,20,16)(13,17,15,14), ( 7, 8, 9,19,20)(13,17,16,15,14), ( 9,10,11,18,17,16,15,14,13), (11,12,13,18)(14,17,16,15), (), (13,16,15,14)(17,20,19,18), ( 1, 5, 4, 3, 2)(16,17,18,19,20), ( 1, 2, 8, 7, 6)(16,17,18,19,20), ( 2, 3,10, 9, 8)(16,17,18,19,20), ( 3, 4,12,11,10)(16,17,18,19,20), ( 4, 5,14,13,12)(16,17,18,19,20), ( 1, 6,15,14, 5)(16,17,18,19,20), ( 6, 7,20,15)(16,17,18,19), ( 7, 8, 9,19)(16,17,18,20), ( 9,10,11,18,19,20,16), (11,12,13,17)(16,18,19,20), (13,14,15,16)(17,18,19,20), () ] gap> Length(c); 144 gap> C:=Group(List([1..144],j->c[j])); Error, operations: power of list and integer is not defined at id := arg[1] ^ 0 ... in Group( List( [ 1 .. 144 ], function ( j ) ... end ) ) called from main loop brk> C:=Group(c); Syntax error: warning, undefined global variable in *errin* line 1 C:=Group(c); ^ Error, operations: power of list and integer is not defined at id := arg[1] ^ 0 ... in Group( c ) called from Group( List( [ 1 .. 144 ], function ( j ) ... end ) ) called from main loop brk> quit; gap> C:=Group(c); Error, operations: power of list and integer is not defined at id := arg[1] ^ 0 ... in Group( c ) called from main loop brk> quit; gap> op(c); Error, Variable: 'op' must have a value gap> Group(c,i->i); Error, sorry, the elements of lie in no common ring domain in Domain( Concatenation( gens, [ id ] ) ) called from Group( c, function ( i ) ... end ) called from main loop brk> quit; gap> c; [ (), (1,8,7,6)(2,3,4,5), ( 1, 3, 4, 5)( 2,10, 9, 8), ( 1, 2, 4, 5)( 3,12,11,10), ( 1, 2, 3, 5)( 4,14,13,12), ( 1, 2, 3, 4)( 5, 6,15,14), ( 1, 2, 3, 4, 5)( 6, 7,20,16,15), ( 1, 2, 3, 4, 5)( 7, 8, 9,19,20), ( 1, 2, 3, 4, 5)( 9,10,11,18,17), ( 1, 2, 3, 4, 5)(11,12,13,17,18), ( 1, 2, 3, 4, 5)(13,14,15,16,17), ( 1, 2, 3, 4, 5)(16,20,19,18,17), (1,6,7,8)(2,5,4,3), (), ( 1, 6, 7, 2)( 3,10, 9, 8), ( 1, 6, 7, 8, 2)( 3, 4,12,11,10), ( 1, 6, 7, 8, 2)( 4, 5,14,13,12), ( 1,15,14, 5)( 2, 6, 7, 8), ( 1, 7, 8, 2)( 6,20,16,15), ( 1, 6, 8, 2)( 7, 9,19,20), ( 1, 6, 7, 8, 2)( 9,10,11,18,17), ( 1, 6, 7, 8, 2)(11,12,13,17,18), ( 1, 6, 7, 8, 2)(13,14,15,16,17), ( 1, 6, 7, 8, 2)(16,20,19,18,17), ( 1, 5, 4, 3)( 2, 8, 9,10), ( 1, 2, 7, 6)( 3, 8, 9,10), (), ( 2, 8, 9, 3)( 4,12,11,10), ( 2, 8, 9,10, 3)( 4, 5,14,13,12), ( 1, 6,15,14, 5)( 2, 8, 9,10, 3), ( 2, 8, 9,10, 3)( 6, 7,20,16,15), ( 2, 9,10, 3)( 7, 8,19,20), ( 2, 8,10, 3)( 9,11,18,17), ( 2, 8, 9,10, 3)(11,12,13,17,18), ( 2, 8, 9,10, 3)(13,14,15,16,17), ( 2, 8, 9,10, 3)(16,20,19,18,17), ( 1, 5, 4, 2)( 3,10,11,12), ( 1, 2, 8, 7, 6)( 3,10,11,12, 4), ( 2, 3, 9, 8)( 4,10,11,12), (), ( 3,10,11, 4)( 5,14,13,12), ( 1, 6,15,14, 5)( 3,10,11,12, 4), ( 3,10,11,12, 4)( 6, 7,20,16,15), ( 3,10,11,12, 4)( 7, 8, 9,19,20), ( 3,11,12, 4)( 9,10,18,17), ( 3,10,12, 4)(11,13,17,18), ( 3,10,11,12, 4)(13,14,15,16,17), ( 3,10,11,12, 4)(16,20,19,18,17), ( 1, 5, 3, 2)( 4,12,13,14), ( 1, 2, 8, 7, 6)( 4,12,13,14, 5), ( 2, 3,10, 9, 8)( 4,12,13,14, 5), ( 3, 4,11,10)( 5,12,13,14), (), ( 1, 6,15,14)( 4,12,13, 5), ( 4,12,13,14, 5)( 6, 7,20,16,15), ( 4,12,13,14, 5)( 7, 8, 9,19,20), ( 4,12,13,14, 5)( 9,10,11,18,17), ( 4,13,14, 5)(11,12,17,18), ( 4,12,14, 5)(13,15,16,17), ( 4,12,13,14, 5)(16,20,19,18,17), ( 1, 4, 3, 2)( 5,14,15, 6), ( 1, 5,14,15)( 2, 8, 7, 6), ( 1, 5,14,15, 6)( 2, 3,10, 9, 8), ( 1, 5,14,15, 6)( 3, 4,12,11,10), ( 1,14,15, 6)( 4, 5,13,12), (), ( 1, 5,14, 6)( 7,20,16,15), ( 1, 5,14,15, 6)( 7, 8, 9,19,20), ( 1, 5,14,15, 6)( 9,10,11,18,17), ( 1, 5,14,15, 6)(11,12,13,17,18), ( 1, 5,15, 6)(13,14,16,17), ( 1, 5,14,15, 6)(16,20,19,18,17), ( 1, 5, 4, 3, 2)( 6,15,16,20, 7), ( 1, 2, 8, 7)( 6,15,16,20), ( 2, 3,10, 9, 8)( 6,15,16,20, 7), ( 3, 4,12,11,10)( 6,15,16,20, 7), ( 4, 5,14,13,12)( 6,15,16,20, 7), ( 1, 6,14, 5)( 7,15,16,20), (), ( 6,15,16, 7)( 8, 9,19,20), ( 6,15,16,20, 7)( 9,10,11,18,17), ( 6,15,16,20, 7)(11,12,13,17,18), ( 6,16,20, 7)(13,14,15,17), ( 6,15,20, 7)(16,19,18,17), ( 1, 5, 4, 3, 2)( 7,20,19, 9, 8), ( 1, 2, 8, 6)( 7,20,19, 9), ( 2, 3,10, 9)( 7,20,19, 8), ( 3, 4,12,11,10)( 7,20,19, 9, 8), ( 4, 5,14,13,12)( 7,20,19, 9, 8), ( 1, 6,15,14, 5)( 7,20,19, 9, 8), ( 6, 7,16,15)( 8,20,19, 9), (), ( 7,20,19,10,11,18,17, 9, 8), ( 7,20,19, 9, 8)(11,12,13,17,18), ( 7,20,19, 9, 8)(13,14,15,16,17), ( 7,19, 9, 8)(16,20,18,17), ( 1, 5, 4, 3, 2)( 9,17,18,11,10), ( 1, 2, 8, 7, 6)( 9,17,18,11,10), ( 2, 3,10, 8)( 9,17,18,11), ( 3, 4,12,11)( 9,17,18,10), ( 4, 5,14,13,12)( 9,17,18,11,10), ( 1, 6,15,14, 5)( 9,17,18,11,10), ( 6, 7,20,16,15)( 9,17,18,11,10), ( 7, 8, 9,17,18,11,10,19,20), (), ( 9,18,12,13,17,11,10), ( 9,13,14,15,16,17,18,11,10), ( 9,16,20,19,18,11,10), ( 1, 5, 4, 3, 2)(11,18,17,13,12), ( 1, 2, 8, 7, 6)(11,18,17,13,12), ( 2, 3,10, 9, 8)(11,18,17,13,12), ( 3, 4,12,10)(11,18,17,13), ( 4, 5,14,13)(11,18,17,12), ( 1, 6,15,14, 5)(11,18,17,13,12), ( 6, 7,20,16,15)(11,18,17,13,12), ( 7, 8, 9,19,20)(11,18,17,13,12), ( 9,10,11,17,13,12,18), (), (11,18,13,12)(14,15,16,17), (11,17,13,12)(16,20,19,18), ( 1, 5, 4, 3, 2)(13,17,16,15,14), ( 1, 2, 8, 7, 6)(13,17,16,15,14), ( 2, 3,10, 9, 8)(13,17,16,15,14), ( 3, 4,12,11,10)(13,17,16,15,14), ( 4, 5,14,12)(13,17,16,15), ( 1, 6,15, 5)(13,17,16,14), ( 6, 7,20,16)(13,17,15,14), ( 7, 8, 9,19,20)(13,17,16,15,14), ( 9,10,11,18,17,16,15,14,13), (11,12,13,18)(14,17,16,15), (), (13,16,15,14)(17,20,19,18), ( 1, 5, 4, 3, 2)(16,17,18,19,20), ( 1, 2, 8, 7, 6)(16,17,18,19,20), ( 2, 3,10, 9, 8)(16,17,18,19,20), ( 3, 4,12,11,10)(16,17,18,19,20), ( 4, 5,14,13,12)(16,17,18,19,20), ( 1, 6,15,14, 5)(16,17,18,19,20), ( 6, 7,20,15)(16,17,18,19), ( 7, 8, 9,19)(16,17,18,20), ( 9,10,11,18,19,20,16), (11,12,13,17)(16,18,19,20), (13,14,15,16)(17,18,19,20), () ] gap> C:=Group(c[1],c[2]); Group( (1,8,7,6)(2,3,4,5) ) gap> C:=Group(c[1..144]); Syntax error: ] expected C:=Group(c[1..144]); ^ gap> C:=Group(Set([1..144],i->c[i])); Error, usage: Set( ) gap> quit;