p-group, metabelian, nilpotent (class 2), monomial
Aliases: C23.63C23, C4⋊C4⋊5C4, C2.6(C4×D4), C2.3(C4×Q8), (C2×C4).99D4, (C2×C4).10Q8, (C2×C42).4C2, C22.36(C2×D4), C2.3(C22⋊Q8), C22.13(C2×Q8), C2.2(C42.C2), C2.9(C42⋊C2), C2.2(C42⋊2C2), C22.21(C4○D4), C2.C42.5C2, C22.36(C22×C4), (C22×C4).22C22, C2.4(C22.D4), (C2×C4⋊C4).6C2, (C2×C4).16(C2×C4), SmallGroup(64,68)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
Generators and relations for C23.63C23
G = < a,b,c,d,e,f | a2=b2=c2=1, d2=e2=c, f2=a, ab=ba, ac=ca, ede-1=ad=da, ae=ea, af=fa, bc=cb, fdf-1=bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, ef=fe >
Subgroups: 113 in 77 conjugacy classes, 45 normal (31 characteristic)
C1, C2, C4, C22, C2×C4, C2×C4, C23, C42, C4⋊C4, C4⋊C4, C22×C4, C2.C42, C2×C42, C2×C4⋊C4, C23.63C23
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, C22×C4, C2×D4, C2×Q8, C4○D4, C42⋊C2, C4×D4, C4×Q8, C22⋊Q8, C22.D4, C42.C2, C42⋊2C2, C23.63C23
Character table of C23.63C23
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 4R | 4S | 4T | |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | |
| 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | linear of order 2 |
| ρ9 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | i | -i | 1 | -1 | 1 | -i | i | -i | i | -i | i | -i | -1 | 1 | i | -i | i | 1 | -1 | linear of order 4 |
| ρ10 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -i | -i | -1 | 1 | -1 | i | -i | i | i | -i | i | i | 1 | 1 | i | -i | -i | -1 | -1 | linear of order 4 |
| ρ11 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | i | -i | 1 | -1 | 1 | -i | i | -i | i | -i | i | i | 1 | -1 | -i | i | -i | -1 | 1 | linear of order 4 |
| ρ12 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -i | -i | -1 | 1 | -1 | i | -i | i | i | -i | i | -i | -1 | -1 | -i | i | i | 1 | 1 | linear of order 4 |
| ρ13 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | i | i | -1 | 1 | -1 | -i | i | -i | -i | i | -i | i | -1 | -1 | i | -i | -i | 1 | 1 | linear of order 4 |
| ρ14 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | -i | i | 1 | -1 | 1 | i | -i | i | -i | i | -i | -i | 1 | -1 | i | -i | i | -1 | 1 | linear of order 4 |
| ρ15 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | i | i | -1 | 1 | -1 | -i | i | -i | -i | i | -i | -i | 1 | 1 | -i | i | i | -1 | -1 | linear of order 4 |
| ρ16 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | -i | i | 1 | -1 | 1 | i | -i | i | -i | i | -i | i | -1 | 1 | -i | i | -i | 1 | -1 | linear of order 4 |
| ρ17 | 2 | -2 | -2 | -2 | 2 | 2 | -2 | 2 | 0 | 2 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ18 | 2 | -2 | -2 | -2 | 2 | 2 | -2 | 2 | 0 | -2 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ19 | 2 | -2 | -2 | 2 | -2 | 2 | 2 | -2 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from Q8, Schur index 2 |
| ρ20 | 2 | -2 | -2 | 2 | -2 | 2 | 2 | -2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from Q8, Schur index 2 |
| ρ21 | 2 | 2 | -2 | 2 | 2 | -2 | -2 | -2 | 0 | 2i | 0 | 0 | 0 | 0 | -2i | -2i | 2i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ22 | 2 | 2 | -2 | 2 | 2 | -2 | -2 | -2 | 0 | -2i | 0 | 0 | 0 | 0 | 2i | 2i | -2i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ23 | 2 | 2 | 2 | -2 | -2 | 2 | -2 | -2 | 2i | 0 | 0 | -2i | -2i | 2i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ24 | 2 | 2 | -2 | -2 | -2 | -2 | 2 | 2 | 0 | 0 | 2i | 0 | 0 | 0 | 0 | 0 | 0 | 2i | -2i | -2i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ25 | 2 | -2 | 2 | 2 | -2 | -2 | -2 | 2 | 2i | 0 | 0 | 2i | -2i | -2i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ26 | 2 | 2 | -2 | -2 | -2 | -2 | 2 | 2 | 0 | 0 | -2i | 0 | 0 | 0 | 0 | 0 | 0 | -2i | 2i | 2i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ27 | 2 | -2 | 2 | 2 | -2 | -2 | -2 | 2 | -2i | 0 | 0 | -2i | 2i | 2i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C4○D4 |
| ρ28 | 2 | 2 | 2 | -2 | -2 | 2 | -2 | -2 | -2i | 0 | 0 | 2i | 2i | -2i | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from C4○D4 |
►Regular action on 64 points
(1 9)(2 10)(3 11)(4 12)(5 38)(6 39)(7 40)(8 37)(13 41)(14 42)(15 43)(16 44)(17 45)(18 46)(19 47)(20 48)(21 49)(22 50)(23 51)(24 52)(25 53)(26 54)(27 55)(28 56)(29 57)(30 58)(31 59)(32 60)(33 63)(34 64)(35 61)(36 62)
(1 51)(2 52)(3 49)(4 50)(5 62)(6 63)(7 64)(8 61)(9 23)(10 24)(11 21)(12 22)(13 27)(14 28)(15 25)(16 26)(17 31)(18 32)(19 29)(20 30)(33 39)(34 40)(35 37)(36 38)(41 55)(42 56)(43 53)(44 54)(45 59)(46 60)(47 57)(48 58)
(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 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 20 4 18)(5 16 7 14)(6 41 8 43)(9 19 11 17)(10 48 12 46)(13 37 15 39)(21 31 23 29)(22 60 24 58)(25 33 27 35)(26 64 28 62)(30 50 32 52)(34 56 36 54)(38 44 40 42)(49 59 51 57)(53 63 55 61)
(1 13 9 41)(2 28 10 56)(3 15 11 43)(4 26 12 54)(5 58 38 30)(6 45 39 17)(7 60 40 32)(8 47 37 19)(14 24 42 52)(16 22 44 50)(18 64 46 34)(20 62 48 36)(21 53 49 25)(23 55 51 27)(29 61 57 35)(31 63 59 33)
G:=sub<Sym(64)| (1,9)(2,10)(3,11)(4,12)(5,38)(6,39)(7,40)(8,37)(13,41)(14,42)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,50)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,59)(32,60)(33,63)(34,64)(35,61)(36,62), (1,51)(2,52)(3,49)(4,50)(5,62)(6,63)(7,64)(8,61)(9,23)(10,24)(11,21)(12,22)(13,27)(14,28)(15,25)(16,26)(17,31)(18,32)(19,29)(20,30)(33,39)(34,40)(35,37)(36,38)(41,55)(42,56)(43,53)(44,54)(45,59)(46,60)(47,57)(48,58), (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), (1,2,3,4)(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)(2,20,4,18)(5,16,7,14)(6,41,8,43)(9,19,11,17)(10,48,12,46)(13,37,15,39)(21,31,23,29)(22,60,24,58)(25,33,27,35)(26,64,28,62)(30,50,32,52)(34,56,36,54)(38,44,40,42)(49,59,51,57)(53,63,55,61), (1,13,9,41)(2,28,10,56)(3,15,11,43)(4,26,12,54)(5,58,38,30)(6,45,39,17)(7,60,40,32)(8,47,37,19)(14,24,42,52)(16,22,44,50)(18,64,46,34)(20,62,48,36)(21,53,49,25)(23,55,51,27)(29,61,57,35)(31,63,59,33)>;
G:=Group( (1,9)(2,10)(3,11)(4,12)(5,38)(6,39)(7,40)(8,37)(13,41)(14,42)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,50)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,59)(32,60)(33,63)(34,64)(35,61)(36,62), (1,51)(2,52)(3,49)(4,50)(5,62)(6,63)(7,64)(8,61)(9,23)(10,24)(11,21)(12,22)(13,27)(14,28)(15,25)(16,26)(17,31)(18,32)(19,29)(20,30)(33,39)(34,40)(35,37)(36,38)(41,55)(42,56)(43,53)(44,54)(45,59)(46,60)(47,57)(48,58), (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), (1,2,3,4)(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)(2,20,4,18)(5,16,7,14)(6,41,8,43)(9,19,11,17)(10,48,12,46)(13,37,15,39)(21,31,23,29)(22,60,24,58)(25,33,27,35)(26,64,28,62)(30,50,32,52)(34,56,36,54)(38,44,40,42)(49,59,51,57)(53,63,55,61), (1,13,9,41)(2,28,10,56)(3,15,11,43)(4,26,12,54)(5,58,38,30)(6,45,39,17)(7,60,40,32)(8,47,37,19)(14,24,42,52)(16,22,44,50)(18,64,46,34)(20,62,48,36)(21,53,49,25)(23,55,51,27)(29,61,57,35)(31,63,59,33) );
G=PermutationGroup([[(1,9),(2,10),(3,11),(4,12),(5,38),(6,39),(7,40),(8,37),(13,41),(14,42),(15,43),(16,44),(17,45),(18,46),(19,47),(20,48),(21,49),(22,50),(23,51),(24,52),(25,53),(26,54),(27,55),(28,56),(29,57),(30,58),(31,59),(32,60),(33,63),(34,64),(35,61),(36,62)], [(1,51),(2,52),(3,49),(4,50),(5,62),(6,63),(7,64),(8,61),(9,23),(10,24),(11,21),(12,22),(13,27),(14,28),(15,25),(16,26),(17,31),(18,32),(19,29),(20,30),(33,39),(34,40),(35,37),(36,38),(41,55),(42,56),(43,53),(44,54),(45,59),(46,60),(47,57),(48,58)], [(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)], [(1,2,3,4),(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),(2,20,4,18),(5,16,7,14),(6,41,8,43),(9,19,11,17),(10,48,12,46),(13,37,15,39),(21,31,23,29),(22,60,24,58),(25,33,27,35),(26,64,28,62),(30,50,32,52),(34,56,36,54),(38,44,40,42),(49,59,51,57),(53,63,55,61)], [(1,13,9,41),(2,28,10,56),(3,15,11,43),(4,26,12,54),(5,58,38,30),(6,45,39,17),(7,60,40,32),(8,47,37,19),(14,24,42,52),(16,22,44,50),(18,64,46,34),(20,62,48,36),(21,53,49,25),(23,55,51,27),(29,61,57,35),(31,63,59,33)]])
C23.63C23 is a maximal subgroup of
C42⋊14Q8 C43⋊2C2 C4×C22.D4 C4×C42⋊2C2 C4×C42.C2 C23.195C24 C24.192C23 C24.547C23 C23.202C24 C24.195C23 C24.198C23 C23.211C24 C42.33Q8 C42⋊4Q8 C23.214C24 C23.215C24 C24.203C23 C24.204C23 C23.218C24 C23.225C24 C23.226C24 C23.227C24 C23.235C24 C23.237C24 C23.238C24 C23.241C24 C24.218C23 C23.250C24 C23.252C24 C23.253C24 C23.255C24 C24.223C23 C24.225C23 C23.259C24 C24.227C23 C23.263C24 C23.264C24 C24.230C23 C24.563C23 C23.321C24 C23.323C24 C24.567C23 C24.267C23 C24.268C23 C24.269C23 C23.344C24 C23.346C24 C23.349C24 C23.350C24 C23.351C24 C23.353C24 C23.356C24 C24.278C23 C24.279C23 C23.359C24 C23.360C24 C23.362C24 C24.283C23 C24.285C23 C24.286C23 C23.367C24 C23.368C24 C23.369C24 C24.289C23 C24.290C23 C24.572C23 C23.374C24 C23.375C24 C24.293C23 C23.377C24 C24.295C23 C23.379C24 C24.573C23 C24.576C23 C23.385C24 C24.577C23 C24.304C23 C23.396C24 C23.397C24 C23.398C24 C24.308C23 C23.405C24 C23.406C24 C23.407C24 C23.408C24 C23.409C24 C23.410C24 C23.411C24 C23.414C24 C24.309C23 C23.416C24 C23.417C24 C23.418C24 C23.419C24 C23.420C24 C24.311C23 C23.422C24 C24.313C23 C23.424C24 C23.425C24 C23.426C24 C24.315C23 C23.428C24 C23.429C24 C23.430C24 C23.431C24 C23.432C24 C23.433C24 C24.326C23 C23.456C24 C23.457C24 C24.332C23 C24.583C23 C42.174D4 C24.584C23 C42.36Q8 C23.473C24 C24.338C23 C24.339C23 C24.340C23 C24.341C23 C23.478C24 C23.479C24 C42.179D4 C23.485C24 C23.486C24 C24.345C23 C23.488C24 C24.346C23 C23.490C24 C23.494C24 C24.347C23 C23.496C24 C24.348C23 C42.183D4 C23.500C24 C42⋊23D4 C23.502C24 C42.184D4 C42⋊8Q8 C42.38Q8 C24.355C23 C23.508C24 C42⋊25D4 C42.185D4 C42⋊9Q8 C23.530C24 C42.191D4 C42.192D4 C24.374C23 C23.548C24 C24.375C23 C23.550C24 C23.551C24 C24.376C23 C23.553C24 C23.554C24 C23.555C24 C24.379C23 C42⋊11Q8 C23.567C24 C23.573C24 C23.574C24 C23.576C24 C24.385C23 C24.393C23 C23.589C24 C23.590C24 C23.591C24 C23.592C24 C24.401C23 C24.403C23 C24.405C23 C23.600C24 C23.605C24 C23.607C24 C24.411C23 C23.611C24 C23.613C24 C24.413C23 C23.615C24 C23.616C24 C23.617C24 C23.619C24 C23.620C24 C23.621C24 C23.622C24 C24.418C23 C23.625C24 C23.626C24 C24.421C23 C23.630C24 C23.631C24 C23.634C24 C23.637C24 C24.426C23 C24.427C23 C23.640C24 C23.641C24 C24.428C23 C23.643C24 C24.430C23 C23.645C24 C24.432C23 C23.647C24 C24.434C23 C24.435C23 C23.651C24 C23.652C24 C23.654C24 C23.655C24 C24.438C23 C23.658C24 C23.659C24 C24.440C23 C23.662C24 C24.443C23 C23.666C24 C23.667C24 C23.668C24 C23.669C24 C24.445C23 C23.671C24 C23.672C24 C23.673C24 C23.674C24 C23.675C24 C23.676C24 C23.677C24 C23.679C24 C24.448C23 C23.681C24 C23.683C24 C24.450C23 C23.686C24 C23.687C24 C23.688C24 C23.689C24 C24.454C23 C23.691C24 C23.692C24 C23.693C24 C23.694C24 C23.695C24 C23.696C24 C23.697C24 C23.698C24 C23.699C24 C23.700C24 C23.702C24 C23.703C24 C23.705C24 C23.706C24 C23.708C24 C23.709C24 C23.710C24 C23.729C24 C23.730C24 C23.731C24 C23.733C24 C23.736C24 C23.738C24 C23.739C24 C42.439D4 C42⋊43D4 C23.753C24 C24.599C23 C42⋊15Q8 C43.18C2 C43⋊4C2 C43⋊5C2
C2p.(C4×D4): C42⋊42D4 C4×C22⋊Q8 C42.159D4 C42.161D4 C23.234C24 C24.558C23 C23.244C24 C23.247C24 ...
C23.63C23 is a maximal quotient of
C24.624C23 C24.626C23 C24.631C23 C24.632C23 C24.633C23 C24.635C23 C4⋊C4⋊3C8 (C2×C8).Q8
C2.(C4×D4p): C2.D8⋊4C4 C2.(C4×D12) C2.(C4×D20) C4⋊Dic7⋊7C4 ...
C2p.(C4×Q8): C4.Q8⋊9C4 C4.Q8⋊10C4 C2.D8⋊5C4 M4(2).3Q8 C6.(C4×D4) C2.(C4×Dic6) Dic3⋊C4⋊C4 (C2×C42).6S3 ...
Matrix representation of C23.63C23 ►in GL5(𝔽5)
| 1 | 0 | 0 | 0 | 0 |
| 0 | 4 | 0 | 0 | 0 |
| 0 | 0 | 4 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 4 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 4 |
| 4 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 4 |
| 2 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 4 | 0 | 0 |
| 0 | 0 | 0 | 3 | 0 |
| 0 | 0 | 0 | 4 | 2 |
| 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 2 | 2 |
| 0 | 0 | 0 | 0 | 3 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 3 | 0 | 0 | 0 |
| 0 | 0 | 3 | 0 | 0 |
| 0 | 0 | 0 | 3 | 3 |
| 0 | 0 | 0 | 0 | 2 |
G:=sub<GL(5,GF(5))| [1,0,0,0,0,0,4,0,0,0,0,0,4,0,0,0,0,0,4,0,0,0,0,0,4],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,4,0,0,0,0,0,4],[4,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,4,0,0,0,0,0,4],[2,0,0,0,0,0,1,0,0,0,0,0,4,0,0,0,0,0,3,4,0,0,0,0,2],[3,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,2,0,0,0,0,2,3],[1,0,0,0,0,0,3,0,0,0,0,0,3,0,0,0,0,0,3,0,0,0,0,3,2] >;
C23.63C23 in GAP, Magma, Sage, TeX
C_2^3._{63}C_2^3 % in TeX
G:=Group("C2^3.63C2^3"); // GroupNames label
G:=SmallGroup(64,68);
// by ID
G=gap.SmallGroup(64,68);
# by ID
G:=PCGroup([6,-2,2,2,-2,2,2,192,121,199,362,50]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=1,d^2=e^2=c,f^2=a,a*b=b*a,a*c=c*a,e*d*e^-1=a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,f*d*f^-1=b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,e*f=f*e>;
// generators/relations
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