p-group, metabelian, nilpotent (class 3), monomial
Aliases: C42.61C23, C4.822- 1+4, C8⋊Q8⋊27C2, C8⋊7D4⋊32C2, C8⋊9D4⋊27C2, C8⋊2D4⋊32C2, C4⋊C4.379D4, D4.Q8⋊42C2, D8⋊C4⋊26C2, D4⋊Q8⋊39C2, (C2×D4).179D4, C2.58(D4○D8), C8.34(C4○D4), C22⋊C4.63D4, C4⋊C4.252C23, C4⋊C8.120C22, (C2×C4).539C24, (C2×C8).106C23, (C2×D8).90C22, C23.344(C2×D4), C4⋊Q8.171C22, C2.92(D4⋊6D4), C8⋊C4.53C22, (C4×D4).179C22, (C2×D4).257C23, C22.D8⋊34C2, C22⋊C8.98C22, M4(2)⋊C4⋊34C2, C2.D8.132C22, C4.Q8.138C22, D4⋊C4.81C22, C4⋊D4.106C22, C23.19D4⋊44C2, C23.25D4⋊30C2, (C22×C8).290C22, C22.799(C22×D4), C42.C2.52C22, C2.94(D8⋊C22), C22.49C24⋊9C2, (C22×C4).1167C23, C22.47C24⋊10C2, C42⋊C2.210C22, (C2×M4(2)).132C22, C4.121(C2×C4○D4), (C2×C4).623(C2×D4), (C2×C4⋊C4).688C22, SmallGroup(128,2079)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
Generators and relations for C42.61C23
G = < a,b,c,d,e | a4=b4=e2=1, c2=d2=a2b2, ab=ba, cac-1=eae=a-1b2, dad-1=ab2, cbc-1=dbd-1=b-1, be=eb, dcd-1=bc, ece=a2b2c, ede=b2d >
Subgroups: 360 in 180 conjugacy classes, 86 normal (84 characteristic)
C1, C2, C2, C4, C4, 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), D8, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C8⋊C4, C22⋊C8, D4⋊C4, C4⋊C8, C4.Q8, C2.D8, C2×C4⋊C4, C42⋊C2, C42⋊C2, C4×D4, C4×D4, C4⋊D4, C4⋊D4, C22.D4, C4.4D4, C42.C2, C42⋊2C2, C4⋊Q8, C22×C8, C2×M4(2), C2×D8, C23.25D4, M4(2)⋊C4, C8⋊9D4, D8⋊C4, C8⋊7D4, C8⋊2D4, D4⋊Q8, D4.Q8, C22.D8, C23.19D4, C8⋊Q8, C22.47C24, C22.49C24, C42.61C23
Quotients: C1, C2, C22, D4, C23, C2×D4, C4○D4, C24, C22×D4, C2×C4○D4, 2- 1+4, D4⋊6D4, D8⋊C22, D4○D8, C42.61C23
Character table of C42.61C23
| 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 | 4 | 4 | 8 | 8 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 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 | 0 | 0 | -2 | -2 | -2 | -2 | 0 | -2 | 0 | 0 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ18 | 2 | 2 | 2 | 2 | -2 | -2 | 0 | 0 | -2 | -2 | 2 | 2 | 0 | -2 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ19 | 2 | 2 | 2 | 2 | 2 | -2 | 0 | 0 | -2 | -2 | -2 | -2 | 0 | 2 | 0 | 0 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ20 | 2 | 2 | 2 | 2 | -2 | 2 | 0 | 0 | -2 | -2 | 2 | 2 | 0 | 2 | 0 | 0 | -2 | -2 | 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 | 0 | 0 | -2i | 0 | 2i | 2i | 0 | 0 | -2i | 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 | 0 | 0 | 2i | 0 | 2i | -2i | 0 | 0 | -2i | 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 | 0 | 0 | 2i | 0 | -2i | -2i | 0 | 0 | 2i | 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 | 0 | 0 | -2i | 0 | -2i | 2i | 0 | 0 | 2i | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ25 | 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 | orthogonal lifted from D4○D8 |
| ρ26 | 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 | orthogonal lifted from D4○D8 |
| 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 | 4i | -4i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from D8⋊C22 |
| ρ29 | 4 | -4 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | -4i | 4i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from D8⋊C22 |
►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 36 12 31)(2 33 9 32)(3 34 10 29)(4 35 11 30)(5 58 18 42)(6 59 19 43)(7 60 20 44)(8 57 17 41)(13 52 28 39)(14 49 25 40)(15 50 26 37)(16 51 27 38)(21 54 61 48)(22 55 62 45)(23 56 63 46)(24 53 64 47)
(1 56 10 48)(2 45 11 53)(3 54 12 46)(4 47 9 55)(5 39 20 50)(6 51 17 40)(7 37 18 52)(8 49 19 38)(13 60 26 42)(14 43 27 57)(15 58 28 44)(16 41 25 59)(21 31 63 34)(22 35 64 32)(23 29 61 36)(24 33 62 30)
(1 11 10 2)(3 9 12 4)(5 41 20 59)(6 58 17 44)(7 43 18 57)(8 60 19 42)(13 14 26 27)(15 16 28 25)(21 55 63 47)(22 46 64 54)(23 53 61 45)(24 48 62 56)(29 32 36 35)(30 34 33 31)(37 51 52 40)(38 39 49 50)
(1 27)(2 15)(3 25)(4 13)(5 24)(6 63)(7 22)(8 61)(9 26)(10 14)(11 28)(12 16)(17 21)(18 64)(19 23)(20 62)(29 49)(30 39)(31 51)(32 37)(33 50)(34 40)(35 52)(36 38)(41 54)(42 47)(43 56)(44 45)(46 59)(48 57)(53 58)(55 60)
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), (1,36,12,31)(2,33,9,32)(3,34,10,29)(4,35,11,30)(5,58,18,42)(6,59,19,43)(7,60,20,44)(8,57,17,41)(13,52,28,39)(14,49,25,40)(15,50,26,37)(16,51,27,38)(21,54,61,48)(22,55,62,45)(23,56,63,46)(24,53,64,47), (1,56,10,48)(2,45,11,53)(3,54,12,46)(4,47,9,55)(5,39,20,50)(6,51,17,40)(7,37,18,52)(8,49,19,38)(13,60,26,42)(14,43,27,57)(15,58,28,44)(16,41,25,59)(21,31,63,34)(22,35,64,32)(23,29,61,36)(24,33,62,30), (1,11,10,2)(3,9,12,4)(5,41,20,59)(6,58,17,44)(7,43,18,57)(8,60,19,42)(13,14,26,27)(15,16,28,25)(21,55,63,47)(22,46,64,54)(23,53,61,45)(24,48,62,56)(29,32,36,35)(30,34,33,31)(37,51,52,40)(38,39,49,50), (1,27)(2,15)(3,25)(4,13)(5,24)(6,63)(7,22)(8,61)(9,26)(10,14)(11,28)(12,16)(17,21)(18,64)(19,23)(20,62)(29,49)(30,39)(31,51)(32,37)(33,50)(34,40)(35,52)(36,38)(41,54)(42,47)(43,56)(44,45)(46,59)(48,57)(53,58)(55,60)>;
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), (1,36,12,31)(2,33,9,32)(3,34,10,29)(4,35,11,30)(5,58,18,42)(6,59,19,43)(7,60,20,44)(8,57,17,41)(13,52,28,39)(14,49,25,40)(15,50,26,37)(16,51,27,38)(21,54,61,48)(22,55,62,45)(23,56,63,46)(24,53,64,47), (1,56,10,48)(2,45,11,53)(3,54,12,46)(4,47,9,55)(5,39,20,50)(6,51,17,40)(7,37,18,52)(8,49,19,38)(13,60,26,42)(14,43,27,57)(15,58,28,44)(16,41,25,59)(21,31,63,34)(22,35,64,32)(23,29,61,36)(24,33,62,30), (1,11,10,2)(3,9,12,4)(5,41,20,59)(6,58,17,44)(7,43,18,57)(8,60,19,42)(13,14,26,27)(15,16,28,25)(21,55,63,47)(22,46,64,54)(23,53,61,45)(24,48,62,56)(29,32,36,35)(30,34,33,31)(37,51,52,40)(38,39,49,50), (1,27)(2,15)(3,25)(4,13)(5,24)(6,63)(7,22)(8,61)(9,26)(10,14)(11,28)(12,16)(17,21)(18,64)(19,23)(20,62)(29,49)(30,39)(31,51)(32,37)(33,50)(34,40)(35,52)(36,38)(41,54)(42,47)(43,56)(44,45)(46,59)(48,57)(53,58)(55,60) );
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)], [(1,36,12,31),(2,33,9,32),(3,34,10,29),(4,35,11,30),(5,58,18,42),(6,59,19,43),(7,60,20,44),(8,57,17,41),(13,52,28,39),(14,49,25,40),(15,50,26,37),(16,51,27,38),(21,54,61,48),(22,55,62,45),(23,56,63,46),(24,53,64,47)], [(1,56,10,48),(2,45,11,53),(3,54,12,46),(4,47,9,55),(5,39,20,50),(6,51,17,40),(7,37,18,52),(8,49,19,38),(13,60,26,42),(14,43,27,57),(15,58,28,44),(16,41,25,59),(21,31,63,34),(22,35,64,32),(23,29,61,36),(24,33,62,30)], [(1,11,10,2),(3,9,12,4),(5,41,20,59),(6,58,17,44),(7,43,18,57),(8,60,19,42),(13,14,26,27),(15,16,28,25),(21,55,63,47),(22,46,64,54),(23,53,61,45),(24,48,62,56),(29,32,36,35),(30,34,33,31),(37,51,52,40),(38,39,49,50)], [(1,27),(2,15),(3,25),(4,13),(5,24),(6,63),(7,22),(8,61),(9,26),(10,14),(11,28),(12,16),(17,21),(18,64),(19,23),(20,62),(29,49),(30,39),(31,51),(32,37),(33,50),(34,40),(35,52),(36,38),(41,54),(42,47),(43,56),(44,45),(46,59),(48,57),(53,58),(55,60)]])
Matrix representation of C42.61C23 ►in GL8(𝔽17)
| 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 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 |
| 0 | 0 | 0 | 0 | 0 | 0 | 13 | 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 | 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 |
| 5 | 0 | 5 | 0 | 0 | 0 | 0 | 0 |
| 0 | 5 | 0 | 5 | 0 | 0 | 0 | 0 |
| 5 | 0 | 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 5 | 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 5 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 5 | 5 |
| 0 | 0 | 0 | 0 | 0 | 0 | 5 | 12 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 16 | 0 | 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 | 0 | 13 |
| 0 | 0 | 0 | 0 | 0 | 0 | 13 | 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 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 13 |
| 0 | 0 | 0 | 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 0 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 |
G:=sub<GL(8,GF(17))| [0,0,1,0,0,0,0,0,0,0,0,16,0,0,0,0,16,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,13,0,0,0,0,0,0,0,0,0,0,13,0,0,0,0,0,0,4,0],[16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,1,0],[5,0,5,0,0,0,0,0,0,5,0,5,0,0,0,0,5,0,12,0,0,0,0,0,0,5,0,12,0,0,0,0,0,0,0,0,5,5,0,0,0,0,0,0,5,12,0,0,0,0,0,0,0,0,5,5,0,0,0,0,0,0,5,12],[0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,13,0,0,0,0,0,0,13,0,0,0,0,0,0,0,0,0,0,13,0,0,0,0,0,0,13,0],[0,0,0,1,0,0,0,0,0,0,16,0,0,0,0,0,0,16,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,13,0,0,0,0,0,0,4,0,0,0,0,0,0,13,0,0,0] >;
C42.61C23 in GAP, Magma, Sage, TeX
C_4^2._{61}C_2^3 % in TeX
G:=Group("C4^2.61C2^3"); // GroupNames label
G:=SmallGroup(128,2079);
// by ID
G=gap.SmallGroup(128,2079);
# by ID
G:=PCGroup([7,-2,2,2,2,-2,2,-2,112,253,758,723,100,346,248,4037,1027,124]);
// Polycyclic
G:=Group<a,b,c,d,e|a^4=b^4=e^2=1,c^2=d^2=a^2*b^2,a*b=b*a,c*a*c^-1=e*a*e=a^-1*b^2,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*b^2*c,e*d*e=b^2*d>;
// generators/relations
Export