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## G = C23.715C24order 128 = 27

### 432nd central stem extension by C23 of C24

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

Series: Derived Chief Lower central Upper central Jennings

 Derived series C1 — C23 — C23.715C24
 Chief series C1 — C2 — C22 — C23 — C22×C4 — C22×D4 — C23⋊2D4 — C23.715C24
 Lower central C1 — C23 — C23.715C24
 Upper central C1 — C23 — C23.715C24
 Jennings C1 — C23 — C23.715C24

Generators and relations for C23.715C24
G = < a,b,c,d,e,f,g | a2=b2=c2=e2=f2=1, d2=g2=a, ab=ba, ac=ca, ede=ad=da, ae=ea, gfg-1=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-1=abe >

Subgroups: 820 in 322 conjugacy classes, 92 normal (8 characteristic)
C1, C2, C2 [×6], C2 [×6], C4 [×12], C22, C22 [×6], C22 [×38], C2×C4 [×4], C2×C4 [×32], D4 [×40], C23, C23 [×2], C23 [×34], C22⋊C4 [×18], C4⋊C4 [×4], C22×C4 [×14], C22×C4 [×2], C2×D4 [×36], C24, C24 [×4], C2.C42 [×8], C2×C22⋊C4 [×14], C2×C4⋊C4 [×2], C4⋊D4 [×8], C23×C4, C22×D4 [×10], C23.34D4, C232D4 [×8], C23.11D4 [×4], C2×C4⋊D4 [×2], C23.715C24
Quotients: C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], C2×D4 [×6], C24, C22×D4, 2+ 1+4 [×6], C233D4, C22.29C24 [×2], C22.54C24 [×4], C23.715C24

Character table of C23.715C24

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

Smallest permutation representation of C23.715C24
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 20)(6 17)(7 18)(8 19)(9 57)(10 58)(11 59)(12 60)(13 25)(14 26)(15 27)(16 28)(21 34)(22 35)(23 36)(24 33)(29 45)(30 46)(31 47)(32 48)(37 56)(38 53)(39 54)(40 55)(49 61)(50 62)(51 63)(52 64)
(1 11)(2 12)(3 9)(4 10)(5 50)(6 51)(7 52)(8 49)(13 31)(14 32)(15 29)(16 30)(17 63)(18 64)(19 61)(20 62)(21 40)(22 37)(23 38)(24 39)(25 47)(26 48)(27 45)(28 46)(33 54)(34 55)(35 56)(36 53)(41 59)(42 60)(43 57)(44 58)
(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 61)(2 64)(3 63)(4 62)(5 58)(6 57)(7 60)(8 59)(9 17)(10 20)(11 19)(12 18)(13 21)(14 24)(15 23)(16 22)(25 34)(26 33)(27 36)(28 35)(29 38)(30 37)(31 40)(32 39)(41 49)(42 52)(43 51)(44 50)(45 53)(46 56)(47 55)(48 54)
(1 25)(2 14)(3 27)(4 16)(5 35)(6 23)(7 33)(8 21)(9 45)(10 30)(11 47)(12 32)(13 41)(15 43)(17 36)(18 24)(19 34)(20 22)(26 42)(28 44)(29 57)(31 59)(37 62)(38 51)(39 64)(40 49)(46 58)(48 60)(50 56)(52 54)(53 63)(55 61)
(1 27 3 25)(2 28 4 26)(5 56 7 54)(6 53 8 55)(9 47 11 45)(10 48 12 46)(13 41 15 43)(14 42 16 44)(17 38 19 40)(18 39 20 37)(21 63 23 61)(22 64 24 62)(29 57 31 59)(30 58 32 60)(33 50 35 52)(34 51 36 49)```

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

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

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

Matrix representation of C23.715C24 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 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
,
 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
,
 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 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 3 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2
,
 1 3 0 0 0 0 0 0 0 0 0 4 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 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
,
 4 0 0 0 0 0 0 0 0 0 4 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 1 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 1 2 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 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 0 4 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 4 3 0 0 0 0 0 0 0 0 1 1

`G:=sub<GL(10,GF(5))| [1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4],[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],[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],[4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,2],[1,0,0,0,0,0,0,0,0,0,3,4,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0],[4,4,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,2,4,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,2,4],[4,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,1,4,0,0,0,0,0,0,0,0,2,4,0,0,0,0,0,0,0,0,0,0,4,1,0,0,0,0,0,0,0,0,3,1] >;`

C23.715C24 in GAP, Magma, Sage, TeX

`C_2^3._{715}C_2^4`
`% in TeX`

`G:=Group("C2^3.715C2^4");`
`// GroupNames label`

`G:=SmallGroup(128,1547);`
`// by ID`

`G=gap.SmallGroup(128,1547);`
`# by ID`

`G:=PCGroup([7,-2,2,2,2,-2,2,2,112,253,758,723,794,185,80]);`
`// Polycyclic`

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

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