p-group, metabelian, nilpotent (class 3), monomial
Aliases: C42.59C23, C4.802- 1+4, C8⋊Q8⋊25C2, C8⋊10(C4○D4), C8⋊7D4⋊31C2, C8⋊9D4⋊25C2, C8⋊2D4⋊31C2, C4⋊C4.167D4, D4.Q8⋊41C2, D8⋊C4⋊25C2, D4⋊6D4⋊15C2, D4⋊2Q8⋊21C2, (C2×D4).331D4, C22⋊C4.62D4, C4⋊C4.250C23, C4⋊C8.118C22, (C2×C4).537C24, (C2×C8).365C23, (C2×D8).89C22, C23.343(C2×D4), C4⋊Q8.169C22, C2.90(D4⋊6D4), C8⋊C4.51C22, C2.90(D4○SD16), (C4×D4).177C22, (C2×D4).255C23, C22.D8⋊32C2, C22⋊C8.96C22, M4(2)⋊C4⋊32C2, C2.D8.130C22, C4.Q8.137C22, D4⋊C4.79C22, C4⋊D4.104C22, C23.19D4⋊43C2, C23.46D4⋊20C2, C22.13(C8⋊C22), (C22×C4).341C23, (C22×C8).288C22, C22.797(C22×D4), C42.C2.50C22, C22.47C24⋊9C2, C42⋊C2.208C22, (C2×M4(2)).130C22, (C2×C4.Q8)⋊13C2, C4.119(C2×C4○D4), (C2×C4).621(C2×D4), C2.83(C2×C8⋊C22), (C2×C4⋊C4).686C22, SmallGroup(128,2077)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
Generators and relations for C42.59C23
G = < a,b,c,d,e | a4=b4=1, c2=a2, d2=a2b2, e2=b2, ab=ba, cac-1=eae-1=a-1b2, dad-1=ab2, cbc-1=dbd-1=b-1, be=eb, dcd-1=bc, ece-1=a2b2c, ede-1=b2d >
Subgroups: 392 in 194 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), D8, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, C8⋊C4, C22⋊C8, D4⋊C4, C4⋊C8, C4.Q8, C2.D8, C2×C4⋊C4, C42⋊C2, C4×D4, C4×D4, C4⋊D4, C4⋊D4, C22⋊Q8, C22.D4, C42.C2, C42⋊2C2, C4⋊Q8, C22×C8, C2×M4(2), C2×D8, C2×C4○D4, C2×C4.Q8, M4(2)⋊C4, C8⋊9D4, D8⋊C4, C8⋊7D4, C8⋊2D4, D4⋊2Q8, D4.Q8, C22.D8, C23.46D4, C23.19D4, C8⋊Q8, D4⋊6D4, C22.47C24, C42.59C23
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, D4○SD16, C42.59C23
Character table of C42.59C23
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 8A | 8B | 8C | 8D | 8E | 8F | |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 8 | 8 | 2 | 2 | 4 | 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 | -2 | 0 | 0 | -2 | -2 | 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 | 0 | -2 | -2 | 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 | 0 | -2 | -2 | -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 | 0 | -2 | -2 | -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 | 0 | -2 | 2 | 0 | 0 | -2i | 0 | 0 | -2i | 2i | 2i | 0 | 0 | 0 | 0 | 0 | 2 | 0 | -2 | 0 | 0 | complex lifted from C4○D4 |
| ρ22 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | 2i | 0 | 0 | 2i | -2i | -2i | 0 | 0 | 0 | 0 | 0 | 2 | 0 | -2 | 0 | 0 | complex lifted from C4○D4 |
| ρ23 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | -2i | 0 | 0 | 2i | 2i | -2i | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 2 | 0 | 0 | complex lifted from C4○D4 |
| ρ24 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | 2i | 0 | 0 | -2i | -2i | 2i | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 2 | 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 | 0 | 4 | -4 | 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 | 2√-2 | 0 | 0 | 0 | complex lifted from D4○SD16 |
| 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 | -2√-2 | 0 | 0 | 0 | complex lifted from D4○SD16 |
►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 46 3 48)(2 55 4 53)(5 39 7 37)(6 51 8 49)(9 45 11 47)(10 54 12 56)(13 44 15 42)(14 59 16 57)(17 40 19 38)(18 52 20 50)(21 31 23 29)(22 35 24 33)(25 43 27 41)(26 58 28 60)(30 64 32 62)(34 61 36 63)
(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 12 16)(2 15 9 26)(3 25 10 14)(4 13 11 28)(5 64 18 24)(6 23 19 63)(7 62 20 22)(8 21 17 61)(29 49 34 40)(30 39 35 52)(31 51 36 38)(32 37 33 50)(41 48 57 54)(42 53 58 47)(43 46 59 56)(44 55 60 45)
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), (1,46,3,48)(2,55,4,53)(5,39,7,37)(6,51,8,49)(9,45,11,47)(10,54,12,56)(13,44,15,42)(14,59,16,57)(17,40,19,38)(18,52,20,50)(21,31,23,29)(22,35,24,33)(25,43,27,41)(26,58,28,60)(30,64,32,62)(34,61,36,63), (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), (1,27,12,16)(2,15,9,26)(3,25,10,14)(4,13,11,28)(5,64,18,24)(6,23,19,63)(7,62,20,22)(8,21,17,61)(29,49,34,40)(30,39,35,52)(31,51,36,38)(32,37,33,50)(41,48,57,54)(42,53,58,47)(43,46,59,56)(44,55,60,45)>;
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), (1,46,3,48)(2,55,4,53)(5,39,7,37)(6,51,8,49)(9,45,11,47)(10,54,12,56)(13,44,15,42)(14,59,16,57)(17,40,19,38)(18,52,20,50)(21,31,23,29)(22,35,24,33)(25,43,27,41)(26,58,28,60)(30,64,32,62)(34,61,36,63), (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), (1,27,12,16)(2,15,9,26)(3,25,10,14)(4,13,11,28)(5,64,18,24)(6,23,19,63)(7,62,20,22)(8,21,17,61)(29,49,34,40)(30,39,35,52)(31,51,36,38)(32,37,33,50)(41,48,57,54)(42,53,58,47)(43,46,59,56)(44,55,60,45) );
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)], [(1,46,3,48),(2,55,4,53),(5,39,7,37),(6,51,8,49),(9,45,11,47),(10,54,12,56),(13,44,15,42),(14,59,16,57),(17,40,19,38),(18,52,20,50),(21,31,23,29),(22,35,24,33),(25,43,27,41),(26,58,28,60),(30,64,32,62),(34,61,36,63)], [(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)], [(1,27,12,16),(2,15,9,26),(3,25,10,14),(4,13,11,28),(5,64,18,24),(6,23,19,63),(7,62,20,22),(8,21,17,61),(29,49,34,40),(30,39,35,52),(31,51,36,38),(32,37,33,50),(41,48,57,54),(42,53,58,47),(43,46,59,56),(44,55,60,45)]])
Matrix representation of C42.59C23 ►in GL8(𝔽17)
| 0 | 0 | 16 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 16 | 16 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 13 | 13 | 13 | 9 |
| 0 | 0 | 0 | 0 | 13 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 4 | 0 | 4 |
| 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 | 16 | 16 | 16 | 15 |
| 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 |
| 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 13 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 14 | 11 | 11 |
| 0 | 0 | 0 | 0 | 14 | 14 | 0 | 11 |
| 0 | 0 | 0 | 0 | 14 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 0 | 3 | 6 |
| 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 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 4 | 4 | 4 | 8 |
| 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 0 | 13 | 13 |
| 0 | 0 | 16 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| 1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 |
| 16 | 16 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 4 | 4 | 0 | 4 |
G:=sub<GL(8,GF(17))| [0,0,1,16,0,0,0,0,0,0,0,16,0,0,0,0,16,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,13,13,4,0,0,0,0,0,13,0,4,0,0,0,0,4,13,0,0,0,0,0,0,0,9,0,4],[16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,0,0,16,16,1,0,0,0,0,1,0,16,0,0,0,0,0,0,0,16,1,0,0,0,0,0,0,15,1],[13,0,0,0,0,0,0,0,0,13,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,14,14,14,3,0,0,0,0,14,14,3,0,0,0,0,0,11,0,0,3,0,0,0,0,11,11,0,6],[0,0,16,0,0,0,0,0,0,0,0,16,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,4,4,13,0,0,0,0,0,4,0,0,0,0,0,0,4,4,0,13,0,0,0,0,0,8,0,13],[0,0,1,16,0,0,0,0,0,0,2,16,0,0,0,0,16,1,0,0,0,0,0,0,15,1,0,0,0,0,0,0,0,0,0,0,13,0,0,4,0,0,0,0,0,13,0,4,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4] >;
C42.59C23 in GAP, Magma, Sage, TeX
C_4^2._{59}C_2^3 % in TeX
G:=Group("C4^2.59C2^3"); // GroupNames label
G:=SmallGroup(128,2077);
// by ID
G=gap.SmallGroup(128,2077);
# by ID
G:=PCGroup([7,-2,2,2,2,-2,2,-2,560,253,456,758,723,100,346,4037,1027,124]);
// Polycyclic
G:=Group<a,b,c,d,e|a^4=b^4=1,c^2=a^2,d^2=a^2*b^2,e^2=b^2,a*b=b*a,c*a*c^-1=e*a*e^-1=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^-1=a^2*b^2*c,e*d*e^-1=b^2*d>;
// generators/relations
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