p-group, metabelian, nilpotent (class 2), monomial, rational
Aliases: C24.462C23, C23.717C24, C22.4902+ 1+4, C22.3742- 1+4, (C22×C4).412D4, C23.227(C2×D4), C2.64(C23⋊3D4), (C22×C4).228C23, (C23×C4).502C22, C22.449(C22×D4), C23.34D4.35C2, C23.11D4.59C2, (C22×Q8).233C22, C23.78C23⋊63C2, C23.83C23⋊131C2, C2.C42.420C22, C2.68(C23.38C23), C2.58(C22.57C24), (C2×C4).434(C2×D4), (C2×C22⋊Q8).48C2, (C2×C4⋊C4).526C22, (C2×C22⋊C4).336C22, SmallGroup(128,1549)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
Generators and relations for C24.462C23
G = < a,b,c,d,e,f,g | a2=b2=c2=1, d2=e2=f2=g2=a, ab=ba, ac=ca, ede-1=ad=da, ae=ea, gfg-1=af=fa, ag=ga, bc=cb, fdf-1=bd=db, be=eb, bf=fb, bg=gb, cd=dc, fef-1=ce=ec, cf=fc, cg=gc, dg=gd, geg-1=abe >
Subgroups: 436 in 222 conjugacy classes, 92 normal (8 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C2×C4, C2×C4, Q8, C23, C23, C23, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×Q8, C24, C2.C42, C2×C22⋊C4, C2×C4⋊C4, C22⋊Q8, C23×C4, C22×Q8, C23.34D4, C23.78C23, C23.11D4, C23.83C23, C2×C22⋊Q8, C24.462C23
Quotients: C1, C2, C22, D4, C23, C2×D4, C24, C22×D4, 2+ 1+4, 2- 1+4, C23⋊3D4, C23.38C23, C22.57C24, C24.462C23
Character table of C24.462C23
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | linear of order 2 |
| ρ17 | 2 | -2 | 2 | -2 | 2 | -2 | 2 | -2 | 2 | -2 | -2 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ18 | 2 | -2 | 2 | -2 | 2 | -2 | 2 | -2 | -2 | 2 | -2 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ19 | 2 | -2 | 2 | -2 | 2 | -2 | 2 | -2 | 2 | -2 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ20 | 2 | -2 | 2 | -2 | 2 | -2 | 2 | -2 | -2 | 2 | 2 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ21 | 4 | -4 | -4 | -4 | 4 | 4 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from 2+ 1+4 |
| ρ22 | 4 | 4 | -4 | 4 | 4 | -4 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from 2+ 1+4 |
| ρ23 | 4 | -4 | 4 | 4 | -4 | -4 | -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 |
| ρ24 | 4 | 4 | 4 | -4 | -4 | 4 | -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 |
| ρ25 | 4 | -4 | -4 | 4 | -4 | 4 | 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 |
| ρ26 | 4 | 4 | -4 | -4 | -4 | -4 | 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 |
►On 64 points
Generators in S64
(1 3)(2 4)(5 7)(6 8)(9 11)(10 12)(13 15)(14 16)(17 19)(18 20)(21 23)(22 24)(25 27)(26 28)(29 31)(30 32)(33 35)(34 36)(37 39)(38 40)(41 43)(42 44)(45 47)(46 48)(49 51)(50 52)(53 55)(54 56)(57 59)(58 60)(61 63)(62 64)
(1 23)(2 24)(3 21)(4 22)(5 11)(6 12)(7 9)(8 10)(13 64)(14 61)(15 62)(16 63)(17 25)(18 26)(19 27)(20 28)(29 33)(30 34)(31 35)(32 36)(37 43)(38 44)(39 41)(40 42)(45 51)(46 52)(47 49)(48 50)(53 57)(54 58)(55 59)(56 60)
(1 27)(2 28)(3 25)(4 26)(5 61)(6 62)(7 63)(8 64)(9 16)(10 13)(11 14)(12 15)(17 21)(18 22)(19 23)(20 24)(29 40)(30 37)(31 38)(32 39)(33 42)(34 43)(35 44)(36 41)(45 57)(46 58)(47 59)(48 60)(49 55)(50 56)(51 53)(52 54)
(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 47 3 45)(2 46 4 48)(5 44 7 42)(6 43 8 41)(9 40 11 38)(10 39 12 37)(13 32 15 30)(14 31 16 29)(17 53 19 55)(18 56 20 54)(21 51 23 49)(22 50 24 52)(25 57 27 59)(26 60 28 58)(33 61 35 63)(34 64 36 62)
(1 32 3 30)(2 33 4 35)(5 48 7 46)(6 51 8 49)(9 52 11 50)(10 47 12 45)(13 59 15 57)(14 56 16 54)(17 43 19 41)(18 38 20 40)(21 34 23 36)(22 31 24 29)(25 37 27 39)(26 44 28 42)(53 64 55 62)(58 61 60 63)
(1 4 3 2)(5 6 7 8)(9 10 11 12)(13 14 15 16)(17 20 19 18)(21 24 23 22)(25 28 27 26)(29 34 31 36)(30 35 32 33)(37 44 39 42)(38 41 40 43)(45 50 47 52)(46 51 48 49)(53 60 55 58)(54 57 56 59)(61 62 63 64)
G:=sub<Sym(64)| (1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36)(37,39)(38,40)(41,43)(42,44)(45,47)(46,48)(49,51)(50,52)(53,55)(54,56)(57,59)(58,60)(61,63)(62,64), (1,23)(2,24)(3,21)(4,22)(5,11)(6,12)(7,9)(8,10)(13,64)(14,61)(15,62)(16,63)(17,25)(18,26)(19,27)(20,28)(29,33)(30,34)(31,35)(32,36)(37,43)(38,44)(39,41)(40,42)(45,51)(46,52)(47,49)(48,50)(53,57)(54,58)(55,59)(56,60), (1,27)(2,28)(3,25)(4,26)(5,61)(6,62)(7,63)(8,64)(9,16)(10,13)(11,14)(12,15)(17,21)(18,22)(19,23)(20,24)(29,40)(30,37)(31,38)(32,39)(33,42)(34,43)(35,44)(36,41)(45,57)(46,58)(47,59)(48,60)(49,55)(50,56)(51,53)(52,54), (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), (1,47,3,45)(2,46,4,48)(5,44,7,42)(6,43,8,41)(9,40,11,38)(10,39,12,37)(13,32,15,30)(14,31,16,29)(17,53,19,55)(18,56,20,54)(21,51,23,49)(22,50,24,52)(25,57,27,59)(26,60,28,58)(33,61,35,63)(34,64,36,62), (1,32,3,30)(2,33,4,35)(5,48,7,46)(6,51,8,49)(9,52,11,50)(10,47,12,45)(13,59,15,57)(14,56,16,54)(17,43,19,41)(18,38,20,40)(21,34,23,36)(22,31,24,29)(25,37,27,39)(26,44,28,42)(53,64,55,62)(58,61,60,63), (1,4,3,2)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,20,19,18)(21,24,23,22)(25,28,27,26)(29,34,31,36)(30,35,32,33)(37,44,39,42)(38,41,40,43)(45,50,47,52)(46,51,48,49)(53,60,55,58)(54,57,56,59)(61,62,63,64)>;
G:=Group( (1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36)(37,39)(38,40)(41,43)(42,44)(45,47)(46,48)(49,51)(50,52)(53,55)(54,56)(57,59)(58,60)(61,63)(62,64), (1,23)(2,24)(3,21)(4,22)(5,11)(6,12)(7,9)(8,10)(13,64)(14,61)(15,62)(16,63)(17,25)(18,26)(19,27)(20,28)(29,33)(30,34)(31,35)(32,36)(37,43)(38,44)(39,41)(40,42)(45,51)(46,52)(47,49)(48,50)(53,57)(54,58)(55,59)(56,60), (1,27)(2,28)(3,25)(4,26)(5,61)(6,62)(7,63)(8,64)(9,16)(10,13)(11,14)(12,15)(17,21)(18,22)(19,23)(20,24)(29,40)(30,37)(31,38)(32,39)(33,42)(34,43)(35,44)(36,41)(45,57)(46,58)(47,59)(48,60)(49,55)(50,56)(51,53)(52,54), (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), (1,47,3,45)(2,46,4,48)(5,44,7,42)(6,43,8,41)(9,40,11,38)(10,39,12,37)(13,32,15,30)(14,31,16,29)(17,53,19,55)(18,56,20,54)(21,51,23,49)(22,50,24,52)(25,57,27,59)(26,60,28,58)(33,61,35,63)(34,64,36,62), (1,32,3,30)(2,33,4,35)(5,48,7,46)(6,51,8,49)(9,52,11,50)(10,47,12,45)(13,59,15,57)(14,56,16,54)(17,43,19,41)(18,38,20,40)(21,34,23,36)(22,31,24,29)(25,37,27,39)(26,44,28,42)(53,64,55,62)(58,61,60,63), (1,4,3,2)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,20,19,18)(21,24,23,22)(25,28,27,26)(29,34,31,36)(30,35,32,33)(37,44,39,42)(38,41,40,43)(45,50,47,52)(46,51,48,49)(53,60,55,58)(54,57,56,59)(61,62,63,64) );
G=PermutationGroup([[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12),(13,15),(14,16),(17,19),(18,20),(21,23),(22,24),(25,27),(26,28),(29,31),(30,32),(33,35),(34,36),(37,39),(38,40),(41,43),(42,44),(45,47),(46,48),(49,51),(50,52),(53,55),(54,56),(57,59),(58,60),(61,63),(62,64)], [(1,23),(2,24),(3,21),(4,22),(5,11),(6,12),(7,9),(8,10),(13,64),(14,61),(15,62),(16,63),(17,25),(18,26),(19,27),(20,28),(29,33),(30,34),(31,35),(32,36),(37,43),(38,44),(39,41),(40,42),(45,51),(46,52),(47,49),(48,50),(53,57),(54,58),(55,59),(56,60)], [(1,27),(2,28),(3,25),(4,26),(5,61),(6,62),(7,63),(8,64),(9,16),(10,13),(11,14),(12,15),(17,21),(18,22),(19,23),(20,24),(29,40),(30,37),(31,38),(32,39),(33,42),(34,43),(35,44),(36,41),(45,57),(46,58),(47,59),(48,60),(49,55),(50,56),(51,53),(52,54)], [(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)], [(1,47,3,45),(2,46,4,48),(5,44,7,42),(6,43,8,41),(9,40,11,38),(10,39,12,37),(13,32,15,30),(14,31,16,29),(17,53,19,55),(18,56,20,54),(21,51,23,49),(22,50,24,52),(25,57,27,59),(26,60,28,58),(33,61,35,63),(34,64,36,62)], [(1,32,3,30),(2,33,4,35),(5,48,7,46),(6,51,8,49),(9,52,11,50),(10,47,12,45),(13,59,15,57),(14,56,16,54),(17,43,19,41),(18,38,20,40),(21,34,23,36),(22,31,24,29),(25,37,27,39),(26,44,28,42),(53,64,55,62),(58,61,60,63)], [(1,4,3,2),(5,6,7,8),(9,10,11,12),(13,14,15,16),(17,20,19,18),(21,24,23,22),(25,28,27,26),(29,34,31,36),(30,35,32,33),(37,44,39,42),(38,41,40,43),(45,50,47,52),(46,51,48,49),(53,60,55,58),(54,57,56,59),(61,62,63,64)]])
Matrix representation of C24.462C23 ►in GL10(𝔽5)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 |
| 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 2 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 4 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
| 0 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 3 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 3 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 3 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 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 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 3 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 4 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
G:=sub<GL(10,GF(5))| [1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4],[4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1],[4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4,4,0,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,0,0,0,0,4,4,0,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,0,0,0,0,4,0,0,1,0,0,0,0,0,0,0,1,4,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,1],[0,2,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,3,3,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,3,0,0,1,0,0,0,0,0,0,0,3,1,0],[0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,3,4,0,0,0,0,0,0,0,0,0,0,4,4,0,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,0,0,0,0,4,0,0,1,0,0,0,0,0,0,0,4,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1] >;
C24.462C23 in GAP, Magma, Sage, TeX
C_2^4._{462}C_2^3 % in TeX
G:=Group("C2^4.462C2^3"); // GroupNames label
G:=SmallGroup(128,1549);
// by ID
G=gap.SmallGroup(128,1549);
# by ID
G:=PCGroup([7,-2,2,2,2,-2,2,2,112,253,120,758,723,100,794,185,80]);
// Polycyclic
G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=1,d^2=e^2=f^2=g^2=a,a*b=b*a,a*c=c*a,e*d*e^-1=a*d=d*a,a*e=e*a,g*f*g^-1=a*f=f*a,a*g=g*a,b*c=c*b,f*d*f^-1=b*d=d*b,b*e=e*b,b*f=f*b,b*g=g*b,c*d=d*c,f*e*f^-1=c*e=e*c,c*f=f*c,c*g=g*c,d*g=g*d,g*e*g^-1=a*b*e>;
// generators/relations
Export