p-group, metabelian, nilpotent (class 3), monomial
Aliases: C42.57C23, C4.782- 1+4, C8⋊Q8⋊23C2, C8⋊9(C4○D4), C8⋊D4⋊50C2, C8⋊9D4⋊24C2, C8⋊8D4⋊21C2, C4⋊C4.165D4, D4.Q8⋊40C2, C4.Q16⋊38C2, (C2×D4).329D4, C2.57(Q8○D8), D4⋊6D4.10C2, C4⋊C8.116C22, C4⋊C4.248C23, (C2×C8).200C23, (C2×C4).535C24, C22⋊C4.175D4, C23.480(C2×D4), C4⋊Q8.167C22, SD16⋊C4⋊39C2, C2.88(D4⋊6D4), C8⋊C4.49C22, C4.Q8.65C22, (C2×D4).254C23, (C4×D4).175C22, C22.D8⋊31C2, C22⋊C8.94C22, (C4×Q8).176C22, (C2×Q8).239C23, M4(2)⋊C4⋊30C2, C2.D8.128C22, D4⋊C4.78C22, C4⋊D4.103C22, C23.48D4⋊31C2, C23.19D4⋊42C2, C23.47D4⋊20C2, C22.10(C8⋊C22), (C22×C4).339C23, (C22×C8).286C22, Q8⋊C4.76C22, (C2×SD16).63C22, C22.795(C22×D4), C22⋊Q8.102C22, C42.C2.48C22, C22.46C24⋊9C2, C42⋊C2.206C22, (C2×M4(2)).128C22, (C2×C2.D8)⋊42C2, C4.117(C2×C4○D4), (C2×C4).619(C2×D4), C2.82(C2×C8⋊C22), (C2×C4⋊C4).684C22, SmallGroup(128,2075)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
Generators and relations for C42.57C23
G = < a,b,c,d,e | a4=b4=e2=1, c2=d2=a2, ab=ba, cac-1=eae=a-1, dad-1=ab2, cbc-1=dbd-1=b-1, be=eb, dcd-1=bc, ece=a2c, ede=b2d >
Subgroups: 352 in 188 conjugacy classes, 88 normal (84 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C8, C8, C2×C4, C2×C4, D4, Q8, C23, C23, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, M4(2), SD16, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C4○D4, C8⋊C4, C22⋊C8, D4⋊C4, Q8⋊C4, C4⋊C8, C4.Q8, C2.D8, C2×C4⋊C4, C42⋊C2, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22⋊Q8, C22.D4, C42.C2, C42.C2, C42⋊2C2, C4⋊Q8, C22×C8, C2×M4(2), C2×SD16, C2×C4○D4, C2×C2.D8, M4(2)⋊C4, C8⋊9D4, SD16⋊C4, C8⋊8D4, C8⋊D4, C4.Q16, D4.Q8, C22.D8, C23.19D4, C23.47D4, C23.48D4, C8⋊Q8, D4⋊6D4, C22.46C24, C42.57C23
Quotients: C1, C2, C22, D4, C23, C2×D4, C4○D4, C24, C8⋊C22, C22×D4, C2×C4○D4, 2- 1+4, D4⋊6D4, C2×C8⋊C22, Q8○D8, C42.57C23
Character table of C42.57C23
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 8A | 8B | 8C | 8D | 8E | 8F | |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 8 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 8 | 4 | 4 | 4 | 4 | 8 | 8 | |
| ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
| ρ2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 2 |
| ρ3 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | 1 | linear of order 2 |
| ρ4 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | 1 | -1 | linear of order 2 |
| ρ5 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | -1 | 1 | linear of order 2 |
| ρ6 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | linear of order 2 |
| ρ7 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 2 |
| ρ8 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 2 |
| ρ9 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | linear of order 2 |
| ρ10 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | linear of order 2 |
| ρ11 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | linear of order 2 |
| ρ12 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | -1 | -1 | 1 | -1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | linear of order 2 |
| ρ13 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | linear of order 2 |
| ρ14 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | linear of order 2 |
| ρ15 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | linear of order 2 |
| ρ16 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | linear of order 2 |
| ρ17 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | 0 | -2 | -2 | 0 | 2 | 2 | 0 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ18 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | -2 | -2 | 0 | 2 | -2 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ19 | 2 | 2 | 2 | 2 | 2 | 2 | -2 | 0 | -2 | -2 | 0 | -2 | -2 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ20 | 2 | 2 | 2 | 2 | -2 | -2 | 2 | 0 | -2 | -2 | 0 | -2 | 2 | 0 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ21 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | -2i | 0 | 0 | 2i | 0 | 0 | 2i | -2i | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ22 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | 2i | 0 | 0 | -2i | 0 | 0 | -2i | 2i | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ23 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | 2i | 0 | 0 | 2i | 0 | 0 | -2i | -2i | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ24 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | -2i | 0 | 0 | -2i | 0 | 0 | 2i | 2i | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ25 | 4 | -4 | -4 | 4 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from C8⋊C22 |
| ρ26 | 4 | -4 | -4 | 4 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from C8⋊C22 |
| ρ27 | 4 | -4 | 4 | -4 | 0 | 0 | 0 | 0 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from 2- 1+4, Schur index 2 |
| ρ28 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2√2 | 0 | 0 | -2√2 | 0 | 0 | symplectic lifted from Q8○D8, Schur index 2 |
| ρ29 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2√2 | 0 | 0 | 2√2 | 0 | 0 | symplectic lifted from Q8○D8, Schur index 2 |
►On 64 points
Generators in S64
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)(17 18 19 20)(21 22 23 24)(25 26 27 28)(29 30 31 32)(33 34 35 36)(37 38 39 40)(41 42 43 44)(45 46 47 48)(49 50 51 52)(53 54 55 56)(57 58 59 60)(61 62 63 64)
(1 23 57 9)(2 24 58 10)(3 21 59 11)(4 22 60 12)(5 47 40 28)(6 48 37 25)(7 45 38 26)(8 46 39 27)(13 33 19 53)(14 34 20 54)(15 35 17 55)(16 36 18 56)(29 61 44 49)(30 62 41 50)(31 63 42 51)(32 64 43 52)
(1 36 3 34)(2 35 4 33)(5 29 7 31)(6 32 8 30)(9 18 11 20)(10 17 12 19)(13 24 15 22)(14 23 16 21)(25 64 27 62)(26 63 28 61)(37 43 39 41)(38 42 40 44)(45 51 47 49)(46 50 48 52)(53 58 55 60)(54 57 56 59)
(1 39 3 37)(2 5 4 7)(6 57 8 59)(9 27 11 25)(10 47 12 45)(13 31 15 29)(14 43 16 41)(17 44 19 42)(18 30 20 32)(21 48 23 46)(22 26 24 28)(33 51 35 49)(34 64 36 62)(38 58 40 60)(50 54 52 56)(53 63 55 61)
(1 36)(2 35)(3 34)(4 33)(5 61)(6 64)(7 63)(8 62)(9 16)(10 15)(11 14)(12 13)(17 24)(18 23)(19 22)(20 21)(25 32)(26 31)(27 30)(28 29)(37 52)(38 51)(39 50)(40 49)(41 46)(42 45)(43 48)(44 47)(53 60)(54 59)(55 58)(56 57)
G:=sub<Sym(64)| (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)(61,62,63,64), (1,23,57,9)(2,24,58,10)(3,21,59,11)(4,22,60,12)(5,47,40,28)(6,48,37,25)(7,45,38,26)(8,46,39,27)(13,33,19,53)(14,34,20,54)(15,35,17,55)(16,36,18,56)(29,61,44,49)(30,62,41,50)(31,63,42,51)(32,64,43,52), (1,36,3,34)(2,35,4,33)(5,29,7,31)(6,32,8,30)(9,18,11,20)(10,17,12,19)(13,24,15,22)(14,23,16,21)(25,64,27,62)(26,63,28,61)(37,43,39,41)(38,42,40,44)(45,51,47,49)(46,50,48,52)(53,58,55,60)(54,57,56,59), (1,39,3,37)(2,5,4,7)(6,57,8,59)(9,27,11,25)(10,47,12,45)(13,31,15,29)(14,43,16,41)(17,44,19,42)(18,30,20,32)(21,48,23,46)(22,26,24,28)(33,51,35,49)(34,64,36,62)(38,58,40,60)(50,54,52,56)(53,63,55,61), (1,36)(2,35)(3,34)(4,33)(5,61)(6,64)(7,63)(8,62)(9,16)(10,15)(11,14)(12,13)(17,24)(18,23)(19,22)(20,21)(25,32)(26,31)(27,30)(28,29)(37,52)(38,51)(39,50)(40,49)(41,46)(42,45)(43,48)(44,47)(53,60)(54,59)(55,58)(56,57)>;
G:=Group( (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)(61,62,63,64), (1,23,57,9)(2,24,58,10)(3,21,59,11)(4,22,60,12)(5,47,40,28)(6,48,37,25)(7,45,38,26)(8,46,39,27)(13,33,19,53)(14,34,20,54)(15,35,17,55)(16,36,18,56)(29,61,44,49)(30,62,41,50)(31,63,42,51)(32,64,43,52), (1,36,3,34)(2,35,4,33)(5,29,7,31)(6,32,8,30)(9,18,11,20)(10,17,12,19)(13,24,15,22)(14,23,16,21)(25,64,27,62)(26,63,28,61)(37,43,39,41)(38,42,40,44)(45,51,47,49)(46,50,48,52)(53,58,55,60)(54,57,56,59), (1,39,3,37)(2,5,4,7)(6,57,8,59)(9,27,11,25)(10,47,12,45)(13,31,15,29)(14,43,16,41)(17,44,19,42)(18,30,20,32)(21,48,23,46)(22,26,24,28)(33,51,35,49)(34,64,36,62)(38,58,40,60)(50,54,52,56)(53,63,55,61), (1,36)(2,35)(3,34)(4,33)(5,61)(6,64)(7,63)(8,62)(9,16)(10,15)(11,14)(12,13)(17,24)(18,23)(19,22)(20,21)(25,32)(26,31)(27,30)(28,29)(37,52)(38,51)(39,50)(40,49)(41,46)(42,45)(43,48)(44,47)(53,60)(54,59)(55,58)(56,57) );
G=PermutationGroup([[(1,2,3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16),(17,18,19,20),(21,22,23,24),(25,26,27,28),(29,30,31,32),(33,34,35,36),(37,38,39,40),(41,42,43,44),(45,46,47,48),(49,50,51,52),(53,54,55,56),(57,58,59,60),(61,62,63,64)], [(1,23,57,9),(2,24,58,10),(3,21,59,11),(4,22,60,12),(5,47,40,28),(6,48,37,25),(7,45,38,26),(8,46,39,27),(13,33,19,53),(14,34,20,54),(15,35,17,55),(16,36,18,56),(29,61,44,49),(30,62,41,50),(31,63,42,51),(32,64,43,52)], [(1,36,3,34),(2,35,4,33),(5,29,7,31),(6,32,8,30),(9,18,11,20),(10,17,12,19),(13,24,15,22),(14,23,16,21),(25,64,27,62),(26,63,28,61),(37,43,39,41),(38,42,40,44),(45,51,47,49),(46,50,48,52),(53,58,55,60),(54,57,56,59)], [(1,39,3,37),(2,5,4,7),(6,57,8,59),(9,27,11,25),(10,47,12,45),(13,31,15,29),(14,43,16,41),(17,44,19,42),(18,30,20,32),(21,48,23,46),(22,26,24,28),(33,51,35,49),(34,64,36,62),(38,58,40,60),(50,54,52,56),(53,63,55,61)], [(1,36),(2,35),(3,34),(4,33),(5,61),(6,64),(7,63),(8,62),(9,16),(10,15),(11,14),(12,13),(17,24),(18,23),(19,22),(20,21),(25,32),(26,31),(27,30),(28,29),(37,52),(38,51),(39,50),(40,49),(41,46),(42,45),(43,48),(44,47),(53,60),(54,59),(55,58),(56,57)]])
Matrix representation of C42.57C23 ►in GL8(𝔽17)
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 16 | 0 | 0 | 0 | 0 | 0 | 0 |
| 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 0 | 0 | 5 |
| 0 | 0 | 0 | 0 | 0 | 5 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 12 | 0 |
| 0 | 0 | 0 | 0 | 5 | 0 | 0 | 12 |
| 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 16 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 16 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 16 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
| 0 | 0 | 16 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 16 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 5 | 5 | 0 |
| 0 | 0 | 0 | 0 | 5 | 0 | 0 | 12 |
| 0 | 0 | 0 | 0 | 5 | 0 | 0 | 5 |
| 0 | 0 | 0 | 0 | 0 | 12 | 5 | 0 |
| 0 | 13 | 0 | 0 | 0 | 0 | 0 | 0 |
| 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 13 | 0 | 0 | 0 | 0 |
| 0 | 0 | 13 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 15 | 15 | 15 |
| 0 | 0 | 0 | 0 | 15 | 15 | 15 | 2 |
| 0 | 0 | 0 | 0 | 15 | 15 | 2 | 15 |
| 0 | 0 | 0 | 0 | 15 | 2 | 15 | 15 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 12 | 0 |
| 0 | 0 | 0 | 0 | 5 | 0 | 0 | 12 |
| 0 | 0 | 0 | 0 | 5 | 0 | 0 | 5 |
| 0 | 0 | 0 | 0 | 0 | 5 | 12 | 0 |
G:=sub<GL(8,GF(17))| [0,0,0,16,0,0,0,0,0,0,16,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,5,0,0,5,0,0,0,0,0,5,12,0,0,0,0,0,0,12,12,0,0,0,0,0,5,0,0,12],[16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,1,0],[0,0,1,0,0,0,0,0,0,0,0,16,0,0,0,0,16,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,5,5,0,0,0,0,0,5,0,0,12,0,0,0,0,5,0,0,5,0,0,0,0,0,12,5,0],[0,13,0,0,0,0,0,0,13,0,0,0,0,0,0,0,0,0,0,13,0,0,0,0,0,0,13,0,0,0,0,0,0,0,0,0,2,15,15,15,0,0,0,0,15,15,15,2,0,0,0,0,15,15,2,15,0,0,0,0,15,2,15,15],[0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,5,5,0,0,0,0,0,12,0,0,5,0,0,0,0,12,0,0,12,0,0,0,0,0,12,5,0] >;
C42.57C23 in GAP, Magma, Sage, TeX
C_4^2._{57}C_2^3 % in TeX
G:=Group("C4^2.57C2^3"); // GroupNames label
G:=SmallGroup(128,2075);
// by ID
G=gap.SmallGroup(128,2075);
# by ID
G:=PCGroup([7,-2,2,2,2,-2,2,-2,112,253,758,723,100,346,4037,1027,124]);
// Polycyclic
G:=Group<a,b,c,d,e|a^4=b^4=e^2=1,c^2=d^2=a^2,a*b=b*a,c*a*c^-1=e*a*e=a^-1,d*a*d^-1=a*b^2,c*b*c^-1=d*b*d^-1=b^-1,b*e=e*b,d*c*d^-1=b*c,e*c*e=a^2*c,e*d*e=b^2*d>;
// generators/relations
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