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G = C24.459C23order 128 = 27

299th non-split extension by C24 of C23 acting via C23/C2=C22

p-group, metabelian, nilpotent (class 2), monomial, rational

Series: Derived Chief Lower central Upper central Jennings

 Derived series C1 — C23 — C24.459C23
 Chief series C1 — C2 — C22 — C23 — C24 — C22×D4 — C23⋊2D4 — C24.459C23
 Lower central C1 — C23 — C24.459C23
 Upper central C1 — C23 — C24.459C23
 Jennings C1 — C23 — C24.459C23

Generators and relations for C24.459C23
G = < a,b,c,d,e,f,g | a2=b2=c2=e2=f2=g2=1, d2=a, ab=ba, ac=ca, ede=ad=da, ae=ea, gfg=af=fa, ag=ga, bc=cb, fdf=bd=db, be=eb, bf=fb, bg=gb, cd=dc, fef=ce=ec, cf=fc, cg=gc, dg=gd, geg=abe >

Subgroups: 692 in 289 conjugacy classes, 92 normal (34 characteristic)
C1, C2 [×3], C2 [×4], C2 [×5], C4 [×13], C22 [×3], C22 [×4], C22 [×31], C2×C4 [×4], C2×C4 [×35], D4 [×24], C23, C23 [×2], C23 [×27], C22⋊C4 [×20], C4⋊C4 [×10], C22×C4 [×5], C22×C4 [×10], C22×C4 [×2], C2×D4 [×22], C24 [×2], C24 [×2], C2.C42 [×2], C2.C42 [×4], C2×C22⋊C4 [×3], C2×C22⋊C4 [×12], C2×C4⋊C4 [×3], C2×C4⋊C4 [×4], C4⋊D4 [×4], C22.D4 [×4], C23×C4, C22×D4 [×2], C22×D4 [×4], C23.7Q8, C232D4, C232D4 [×2], C23.10D4, C23.10D4 [×4], C23.Q8 [×2], C23.4Q8, C23.83C23, C2×C4⋊D4, C2×C22.D4, C24.459C23
Quotients: C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], C2×D4 [×6], C24, C22×D4, 2+ 1+4 [×5], 2- 1+4, C233D4, C22.29C24, C22.31C24, C22.54C24 [×2], C22.56C24 [×2], C24.459C23

Character table of C24.459C23

 class 1 2A 2B 2C 2D 2E 2F 2G 2H 2I 2J 2K 2L 4A 4B 4C 4D 4E 4F 4G 4H 4I 4J 4K 4L 4M size 1 1 1 1 1 1 1 1 4 4 8 8 8 4 4 4 4 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 0 0 0 2 2 -2 -2 0 0 0 0 0 0 0 0 0 orthogonal lifted from D4 ρ18 2 2 -2 -2 2 -2 2 -2 2 -2 0 0 0 2 -2 2 -2 0 0 0 0 0 0 0 0 0 orthogonal lifted from D4 ρ19 2 2 -2 -2 2 -2 2 -2 2 -2 0 0 0 -2 2 -2 2 0 0 0 0 0 0 0 0 0 orthogonal lifted from D4 ρ20 2 2 -2 -2 2 -2 2 -2 -2 2 0 0 0 -2 -2 2 2 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 orthogonal lifted from 2+ 1+4 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 orthogonal lifted from 2+ 1+4 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 orthogonal lifted from 2+ 1+4 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

Smallest permutation representation of C24.459C23
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 41)(2 42)(3 43)(4 44)(5 35)(6 36)(7 33)(8 34)(9 16)(10 13)(11 14)(12 15)(17 50)(18 51)(19 52)(20 49)(21 46)(22 47)(23 48)(24 45)(25 56)(26 53)(27 54)(28 55)(29 60)(30 57)(31 58)(32 59)(37 62)(38 63)(39 64)(40 61)
(1 55)(2 56)(3 53)(4 54)(5 51)(6 52)(7 49)(8 50)(9 60)(10 57)(11 58)(12 59)(13 30)(14 31)(15 32)(16 29)(17 34)(18 35)(19 36)(20 33)(21 61)(22 62)(23 63)(24 64)(25 42)(26 43)(27 44)(28 41)(37 47)(38 48)(39 45)(40 46)
(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 2)(3 4)(5 52)(6 51)(7 50)(8 49)(9 13)(10 16)(11 15)(12 14)(17 33)(18 36)(19 35)(20 34)(21 37)(22 40)(23 39)(24 38)(25 28)(26 27)(29 57)(30 60)(31 59)(32 58)(41 42)(43 44)(45 63)(46 62)(47 61)(48 64)(53 54)(55 56)
(1 38)(2 64)(3 40)(4 62)(5 9)(6 13)(7 11)(8 15)(10 36)(12 34)(14 33)(16 35)(17 59)(18 29)(19 57)(20 31)(21 26)(22 54)(23 28)(24 56)(25 45)(27 47)(30 52)(32 50)(37 44)(39 42)(41 63)(43 61)(46 53)(48 55)(49 58)(51 60)
(1 13)(2 14)(3 15)(4 16)(5 39)(6 40)(7 37)(8 38)(9 44)(10 41)(11 42)(12 43)(17 23)(18 24)(19 21)(20 22)(25 58)(26 59)(27 60)(28 57)(29 54)(30 55)(31 56)(32 53)(33 62)(34 63)(35 64)(36 61)(45 51)(46 52)(47 49)(48 50)```

`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), (1,41)(2,42)(3,43)(4,44)(5,35)(6,36)(7,33)(8,34)(9,16)(10,13)(11,14)(12,15)(17,50)(18,51)(19,52)(20,49)(21,46)(22,47)(23,48)(24,45)(25,56)(26,53)(27,54)(28,55)(29,60)(30,57)(31,58)(32,59)(37,62)(38,63)(39,64)(40,61), (1,55)(2,56)(3,53)(4,54)(5,51)(6,52)(7,49)(8,50)(9,60)(10,57)(11,58)(12,59)(13,30)(14,31)(15,32)(16,29)(17,34)(18,35)(19,36)(20,33)(21,61)(22,62)(23,63)(24,64)(25,42)(26,43)(27,44)(28,41)(37,47)(38,48)(39,45)(40,46), (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), (1,2)(3,4)(5,52)(6,51)(7,50)(8,49)(9,13)(10,16)(11,15)(12,14)(17,33)(18,36)(19,35)(20,34)(21,37)(22,40)(23,39)(24,38)(25,28)(26,27)(29,57)(30,60)(31,59)(32,58)(41,42)(43,44)(45,63)(46,62)(47,61)(48,64)(53,54)(55,56), (1,38)(2,64)(3,40)(4,62)(5,9)(6,13)(7,11)(8,15)(10,36)(12,34)(14,33)(16,35)(17,59)(18,29)(19,57)(20,31)(21,26)(22,54)(23,28)(24,56)(25,45)(27,47)(30,52)(32,50)(37,44)(39,42)(41,63)(43,61)(46,53)(48,55)(49,58)(51,60), (1,13)(2,14)(3,15)(4,16)(5,39)(6,40)(7,37)(8,38)(9,44)(10,41)(11,42)(12,43)(17,23)(18,24)(19,21)(20,22)(25,58)(26,59)(27,60)(28,57)(29,54)(30,55)(31,56)(32,53)(33,62)(34,63)(35,64)(36,61)(45,51)(46,52)(47,49)(48,50)>;`

`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), (1,41)(2,42)(3,43)(4,44)(5,35)(6,36)(7,33)(8,34)(9,16)(10,13)(11,14)(12,15)(17,50)(18,51)(19,52)(20,49)(21,46)(22,47)(23,48)(24,45)(25,56)(26,53)(27,54)(28,55)(29,60)(30,57)(31,58)(32,59)(37,62)(38,63)(39,64)(40,61), (1,55)(2,56)(3,53)(4,54)(5,51)(6,52)(7,49)(8,50)(9,60)(10,57)(11,58)(12,59)(13,30)(14,31)(15,32)(16,29)(17,34)(18,35)(19,36)(20,33)(21,61)(22,62)(23,63)(24,64)(25,42)(26,43)(27,44)(28,41)(37,47)(38,48)(39,45)(40,46), (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), (1,2)(3,4)(5,52)(6,51)(7,50)(8,49)(9,13)(10,16)(11,15)(12,14)(17,33)(18,36)(19,35)(20,34)(21,37)(22,40)(23,39)(24,38)(25,28)(26,27)(29,57)(30,60)(31,59)(32,58)(41,42)(43,44)(45,63)(46,62)(47,61)(48,64)(53,54)(55,56), (1,38)(2,64)(3,40)(4,62)(5,9)(6,13)(7,11)(8,15)(10,36)(12,34)(14,33)(16,35)(17,59)(18,29)(19,57)(20,31)(21,26)(22,54)(23,28)(24,56)(25,45)(27,47)(30,52)(32,50)(37,44)(39,42)(41,63)(43,61)(46,53)(48,55)(49,58)(51,60), (1,13)(2,14)(3,15)(4,16)(5,39)(6,40)(7,37)(8,38)(9,44)(10,41)(11,42)(12,43)(17,23)(18,24)(19,21)(20,22)(25,58)(26,59)(27,60)(28,57)(29,54)(30,55)(31,56)(32,53)(33,62)(34,63)(35,64)(36,61)(45,51)(46,52)(47,49)(48,50) );`

`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)], [(1,41),(2,42),(3,43),(4,44),(5,35),(6,36),(7,33),(8,34),(9,16),(10,13),(11,14),(12,15),(17,50),(18,51),(19,52),(20,49),(21,46),(22,47),(23,48),(24,45),(25,56),(26,53),(27,54),(28,55),(29,60),(30,57),(31,58),(32,59),(37,62),(38,63),(39,64),(40,61)], [(1,55),(2,56),(3,53),(4,54),(5,51),(6,52),(7,49),(8,50),(9,60),(10,57),(11,58),(12,59),(13,30),(14,31),(15,32),(16,29),(17,34),(18,35),(19,36),(20,33),(21,61),(22,62),(23,63),(24,64),(25,42),(26,43),(27,44),(28,41),(37,47),(38,48),(39,45),(40,46)], [(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)], [(1,2),(3,4),(5,52),(6,51),(7,50),(8,49),(9,13),(10,16),(11,15),(12,14),(17,33),(18,36),(19,35),(20,34),(21,37),(22,40),(23,39),(24,38),(25,28),(26,27),(29,57),(30,60),(31,59),(32,58),(41,42),(43,44),(45,63),(46,62),(47,61),(48,64),(53,54),(55,56)], [(1,38),(2,64),(3,40),(4,62),(5,9),(6,13),(7,11),(8,15),(10,36),(12,34),(14,33),(16,35),(17,59),(18,29),(19,57),(20,31),(21,26),(22,54),(23,28),(24,56),(25,45),(27,47),(30,52),(32,50),(37,44),(39,42),(41,63),(43,61),(46,53),(48,55),(49,58),(51,60)], [(1,13),(2,14),(3,15),(4,16),(5,39),(6,40),(7,37),(8,38),(9,44),(10,41),(11,42),(12,43),(17,23),(18,24),(19,21),(20,22),(25,58),(26,59),(27,60),(28,57),(29,54),(30,55),(31,56),(32,53),(33,62),(34,63),(35,64),(36,61),(45,51),(46,52),(47,49),(48,50)])`

Matrix representation of C24.459C23 in GL10(ℤ)

 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 -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 -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 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 0 0 0 -1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 0 0 0 0 0 0 1 0 0 -2 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 0 0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 0 0 0 0 0 0 0 1 0 0 -2 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 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 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 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 -1 1 0 0 0 0 0 0 0 1 0 0 -1

`G:=sub<GL(10,Integers())| [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,-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,-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,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1],[-1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,2,0,0,1,0,0,0,0,0,0,0,-2,-1,0],[-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,-2,0,0,-1,0,0,0,0,0,0,0,-2,-1,0],[0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0],[-1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1] >;`

C24.459C23 in GAP, Magma, Sage, TeX

`C_2^4._{459}C_2^3`
`% in TeX`

`G:=Group("C2^4.459C2^3");`
`// GroupNames label`

`G:=SmallGroup(128,1545);`
`// by ID`

`G=gap.SmallGroup(128,1545);`
`# by ID`

`G:=PCGroup([7,-2,2,2,2,-2,2,2,112,253,758,723,794,185]);`
`// Polycyclic`

`G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=e^2=f^2=g^2=1,d^2=a,a*b=b*a,a*c=c*a,e*d*e=a*d=d*a,a*e=e*a,g*f*g=a*f=f*a,a*g=g*a,b*c=c*b,f*d*f=b*d=d*b,b*e=e*b,b*f=f*b,b*g=g*b,c*d=d*c,f*e*f=c*e=e*c,c*f=f*c,c*g=g*c,d*g=g*d,g*e*g=a*b*e>;`
`// generators/relations`

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