metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3⋊C8⋊2D4, C3⋊1(C8⋊2D4), C4⋊C4.13D6, D6⋊3D4⋊2C2, C12⋊D4⋊4C2, (C2×D4).29D6, C4.161(S3×D4), (C2×C8).170D6, D4⋊C4⋊19S3, C12.111(C2×D4), C2.D24⋊25C2, C12.Q8⋊6C2, C4.27(C4○D12), C12.10(C4○D4), C6.18(C4⋊D4), C2.18(D8⋊S3), C2.11(Q8⋊3D6), C6.36(C8⋊C22), (C2×Dic3).23D4, (C6×D4).43C22, (C22×S3).14D4, C22.180(S3×D4), C2.21(Dic3⋊D4), (C2×C12).222C23, (C2×C24).230C22, (C2×D12).52C22, C4⋊Dic3.75C22, (C2×D4⋊S3)⋊5C2, (C2×C8⋊S3)⋊18C2, (C2×C6).235(C2×D4), (C2×C3⋊C8).20C22, (S3×C2×C4).14C22, (C3×D4⋊C4)⋊30C2, (C3×C4⋊C4).23C22, (C2×C4).329(C22×S3), SmallGroup(192,341)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3⋊C8⋊D4
G = < a,b,c,d | a3=b8=c4=d2=1, bab-1=cac-1=dad=a-1, cbc-1=b3, dbd=b5, dcd=c-1 >
Subgroups: 472 in 130 conjugacy classes, 39 normal (37 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, S3, C6, C6, C8, C2×C4, C2×C4, D4, C23, Dic3, C12, C12, D6, C2×C6, C2×C6, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, M4(2), D8, C22×C4, C2×D4, C2×D4, C3⋊C8, C24, C4×S3, D12, C2×Dic3, C2×Dic3, C3⋊D4, C2×C12, C2×C12, C3×D4, C22×S3, C22×S3, C22×C6, D4⋊C4, D4⋊C4, C4.Q8, C4⋊D4, C2×M4(2), C2×D8, C8⋊S3, C2×C3⋊C8, C4⋊Dic3, D6⋊C4, D4⋊S3, C6.D4, C3×C4⋊C4, C2×C24, S3×C2×C4, C2×D12, C2×D12, C2×C3⋊D4, C6×D4, C8⋊2D4, C12.Q8, C2.D24, C3×D4⋊C4, C12⋊D4, C2×C8⋊S3, C2×D4⋊S3, D6⋊3D4, C3⋊C8⋊D4
Quotients: C1, C2, C22, S3, D4, C23, D6, C2×D4, C4○D4, C22×S3, C4⋊D4, C8⋊C22, C4○D12, S3×D4, C8⋊2D4, Dic3⋊D4, D8⋊S3, Q8⋊3D6, C3⋊C8⋊D4
Character table of C3⋊C8⋊D4
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 3 | 4A | 4B | 4C | 4D | 4E | 6A | 6B | 6C | 6D | 6E | 8A | 8B | 8C | 8D | 12A | 12B | 12C | 12D | 24A | 24B | 24C | 24D | |
| size | 1 | 1 | 1 | 1 | 8 | 12 | 24 | 2 | 2 | 2 | 8 | 12 | 24 | 2 | 2 | 2 | 8 | 8 | 4 | 4 | 12 | 12 | 4 | 4 | 8 | 8 | 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 | 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 | -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 | 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 | -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 | 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 | -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 | 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 | -1 | linear of order 2 |
| ρ9 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ10 | 2 | 2 | 2 | 2 | 0 | -2 | 0 | 2 | -2 | -2 | 0 | 2 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ11 | 2 | 2 | 2 | 2 | -2 | 0 | 0 | -1 | 2 | 2 | -2 | 0 | 0 | -1 | -1 | -1 | 1 | 1 | 2 | 2 | 0 | 0 | -1 | -1 | 1 | 1 | -1 | -1 | -1 | -1 | orthogonal lifted from D6 |
| ρ12 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ13 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | 2 | 2 | -2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -2 | -2 | 0 | 0 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | orthogonal lifted from D6 |
| ρ14 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | 2 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ15 | 2 | 2 | 2 | 2 | 0 | 2 | 0 | 2 | -2 | -2 | 0 | -2 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ16 | 2 | 2 | 2 | 2 | -2 | 0 | 0 | -1 | 2 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | 1 | 1 | -2 | -2 | 0 | 0 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | orthogonal lifted from D6 |
| ρ17 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | -2 | -2 | 2 | 0 | 0 | 2i | -2i | 0 | 0 | -2 | 2 | 0 | 0 | 2i | 2i | -2i | -2i | complex lifted from C4○D4 |
| ρ18 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | -2 | -2 | 2 | 0 | 0 | -2i | 2i | 0 | 0 | -2 | 2 | 0 | 0 | -2i | -2i | 2i | 2i | complex lifted from C4○D4 |
| ρ19 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | -1 | 2 | -2 | 0 | 0 | 0 | 1 | 1 | -1 | √-3 | -√-3 | -2i | 2i | 0 | 0 | 1 | -1 | -√3 | √3 | i | i | -i | -i | complex lifted from C4○D12 |
| ρ20 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | -1 | 2 | -2 | 0 | 0 | 0 | 1 | 1 | -1 | -√-3 | √-3 | 2i | -2i | 0 | 0 | 1 | -1 | -√3 | √3 | -i | -i | i | i | complex lifted from C4○D12 |
| ρ21 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | -1 | 2 | -2 | 0 | 0 | 0 | 1 | 1 | -1 | √-3 | -√-3 | 2i | -2i | 0 | 0 | 1 | -1 | √3 | -√3 | -i | -i | i | i | complex lifted from C4○D12 |
| ρ22 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | -1 | 2 | -2 | 0 | 0 | 0 | 1 | 1 | -1 | -√-3 | √-3 | -2i | 2i | 0 | 0 | 1 | -1 | √3 | -√3 | i | i | -i | -i | complex lifted from C4○D12 |
| ρ23 | 4 | -4 | -4 | 4 | 0 | 0 | 0 | -2 | -4 | 4 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from S3×D4 |
| ρ24 | 4 | -4 | 4 | -4 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 4 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from C8⋊C22 |
| ρ25 | 4 | 4 | 4 | 4 | 0 | 0 | 0 | -2 | -4 | -4 | 0 | 0 | 0 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from S3×D4 |
| ρ26 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | -4 | 4 | -4 | 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 | -2 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | √6 | -√6 | √6 | -√6 | orthogonal lifted from Q8⋊3D6 |
| ρ28 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -√6 | √6 | -√6 | √6 | orthogonal lifted from Q8⋊3D6 |
| ρ29 | 4 | -4 | 4 | -4 | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -√-6 | √-6 | √-6 | -√-6 | complex lifted from D8⋊S3 |
| ρ30 | 4 | -4 | 4 | -4 | 0 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | √-6 | -√-6 | -√-6 | √-6 | complex lifted from D8⋊S3 |
►On 96 points
Generators in S96
(1 46 87)(2 88 47)(3 48 81)(4 82 41)(5 42 83)(6 84 43)(7 44 85)(8 86 45)(9 49 63)(10 64 50)(11 51 57)(12 58 52)(13 53 59)(14 60 54)(15 55 61)(16 62 56)(17 95 34)(18 35 96)(19 89 36)(20 37 90)(21 91 38)(22 39 92)(23 93 40)(24 33 94)(25 66 75)(26 76 67)(27 68 77)(28 78 69)(29 70 79)(30 80 71)(31 72 73)(32 74 65)
(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)(65 66 67 68 69 70 71 72)(73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88)(89 90 91 92 93 94 95 96)
(1 68 13 22)(2 71 14 17)(3 66 15 20)(4 69 16 23)(5 72 9 18)(6 67 10 21)(7 70 11 24)(8 65 12 19)(25 55 90 48)(26 50 91 43)(27 53 92 46)(28 56 93 41)(29 51 94 44)(30 54 95 47)(31 49 96 42)(32 52 89 45)(33 85 79 57)(34 88 80 60)(35 83 73 63)(36 86 74 58)(37 81 75 61)(38 84 76 64)(39 87 77 59)(40 82 78 62)
(1 67)(2 72)(3 69)(4 66)(5 71)(6 68)(7 65)(8 70)(9 17)(10 22)(11 19)(12 24)(13 21)(14 18)(15 23)(16 20)(25 82)(26 87)(27 84)(28 81)(29 86)(30 83)(31 88)(32 85)(33 52)(34 49)(35 54)(36 51)(37 56)(38 53)(39 50)(40 55)(41 75)(42 80)(43 77)(44 74)(45 79)(46 76)(47 73)(48 78)(57 89)(58 94)(59 91)(60 96)(61 93)(62 90)(63 95)(64 92)
G:=sub<Sym(96)| (1,46,87)(2,88,47)(3,48,81)(4,82,41)(5,42,83)(6,84,43)(7,44,85)(8,86,45)(9,49,63)(10,64,50)(11,51,57)(12,58,52)(13,53,59)(14,60,54)(15,55,61)(16,62,56)(17,95,34)(18,35,96)(19,89,36)(20,37,90)(21,91,38)(22,39,92)(23,93,40)(24,33,94)(25,66,75)(26,76,67)(27,68,77)(28,78,69)(29,70,79)(30,80,71)(31,72,73)(32,74,65), (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)(65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88)(89,90,91,92,93,94,95,96), (1,68,13,22)(2,71,14,17)(3,66,15,20)(4,69,16,23)(5,72,9,18)(6,67,10,21)(7,70,11,24)(8,65,12,19)(25,55,90,48)(26,50,91,43)(27,53,92,46)(28,56,93,41)(29,51,94,44)(30,54,95,47)(31,49,96,42)(32,52,89,45)(33,85,79,57)(34,88,80,60)(35,83,73,63)(36,86,74,58)(37,81,75,61)(38,84,76,64)(39,87,77,59)(40,82,78,62), (1,67)(2,72)(3,69)(4,66)(5,71)(6,68)(7,65)(8,70)(9,17)(10,22)(11,19)(12,24)(13,21)(14,18)(15,23)(16,20)(25,82)(26,87)(27,84)(28,81)(29,86)(30,83)(31,88)(32,85)(33,52)(34,49)(35,54)(36,51)(37,56)(38,53)(39,50)(40,55)(41,75)(42,80)(43,77)(44,74)(45,79)(46,76)(47,73)(48,78)(57,89)(58,94)(59,91)(60,96)(61,93)(62,90)(63,95)(64,92)>;
G:=Group( (1,46,87)(2,88,47)(3,48,81)(4,82,41)(5,42,83)(6,84,43)(7,44,85)(8,86,45)(9,49,63)(10,64,50)(11,51,57)(12,58,52)(13,53,59)(14,60,54)(15,55,61)(16,62,56)(17,95,34)(18,35,96)(19,89,36)(20,37,90)(21,91,38)(22,39,92)(23,93,40)(24,33,94)(25,66,75)(26,76,67)(27,68,77)(28,78,69)(29,70,79)(30,80,71)(31,72,73)(32,74,65), (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)(65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88)(89,90,91,92,93,94,95,96), (1,68,13,22)(2,71,14,17)(3,66,15,20)(4,69,16,23)(5,72,9,18)(6,67,10,21)(7,70,11,24)(8,65,12,19)(25,55,90,48)(26,50,91,43)(27,53,92,46)(28,56,93,41)(29,51,94,44)(30,54,95,47)(31,49,96,42)(32,52,89,45)(33,85,79,57)(34,88,80,60)(35,83,73,63)(36,86,74,58)(37,81,75,61)(38,84,76,64)(39,87,77,59)(40,82,78,62), (1,67)(2,72)(3,69)(4,66)(5,71)(6,68)(7,65)(8,70)(9,17)(10,22)(11,19)(12,24)(13,21)(14,18)(15,23)(16,20)(25,82)(26,87)(27,84)(28,81)(29,86)(30,83)(31,88)(32,85)(33,52)(34,49)(35,54)(36,51)(37,56)(38,53)(39,50)(40,55)(41,75)(42,80)(43,77)(44,74)(45,79)(46,76)(47,73)(48,78)(57,89)(58,94)(59,91)(60,96)(61,93)(62,90)(63,95)(64,92) );
G=PermutationGroup([[(1,46,87),(2,88,47),(3,48,81),(4,82,41),(5,42,83),(6,84,43),(7,44,85),(8,86,45),(9,49,63),(10,64,50),(11,51,57),(12,58,52),(13,53,59),(14,60,54),(15,55,61),(16,62,56),(17,95,34),(18,35,96),(19,89,36),(20,37,90),(21,91,38),(22,39,92),(23,93,40),(24,33,94),(25,66,75),(26,76,67),(27,68,77),(28,78,69),(29,70,79),(30,80,71),(31,72,73),(32,74,65)], [(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),(65,66,67,68,69,70,71,72),(73,74,75,76,77,78,79,80),(81,82,83,84,85,86,87,88),(89,90,91,92,93,94,95,96)], [(1,68,13,22),(2,71,14,17),(3,66,15,20),(4,69,16,23),(5,72,9,18),(6,67,10,21),(7,70,11,24),(8,65,12,19),(25,55,90,48),(26,50,91,43),(27,53,92,46),(28,56,93,41),(29,51,94,44),(30,54,95,47),(31,49,96,42),(32,52,89,45),(33,85,79,57),(34,88,80,60),(35,83,73,63),(36,86,74,58),(37,81,75,61),(38,84,76,64),(39,87,77,59),(40,82,78,62)], [(1,67),(2,72),(3,69),(4,66),(5,71),(6,68),(7,65),(8,70),(9,17),(10,22),(11,19),(12,24),(13,21),(14,18),(15,23),(16,20),(25,82),(26,87),(27,84),(28,81),(29,86),(30,83),(31,88),(32,85),(33,52),(34,49),(35,54),(36,51),(37,56),(38,53),(39,50),(40,55),(41,75),(42,80),(43,77),(44,74),(45,79),(46,76),(47,73),(48,78),(57,89),(58,94),(59,91),(60,96),(61,93),(62,90),(63,95),(64,92)]])
Matrix representation of C3⋊C8⋊D4 ►in GL8(𝔽73)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 72 | 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 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 72 | 72 | 2 |
| 0 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 72 |
| 2 | 3 | 0 | 0 | 0 | 0 | 0 | 0 |
| 47 | 71 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 61 | 12 | 56 | 0 |
| 0 | 0 | 0 | 0 | 29 | 68 | 56 | 34 |
| 0 | 0 | 0 | 0 | 29 | 61 | 0 | 24 |
| 0 | 0 | 0 | 0 | 29 | 56 | 12 | 17 |
| 71 | 70 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 2 | 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 | 29 | 61 | 0 | 24 |
| 0 | 0 | 0 | 0 | 12 | 5 | 49 | 24 |
| 0 | 0 | 0 | 0 | 61 | 12 | 56 | 0 |
| 0 | 0 | 0 | 0 | 44 | 17 | 61 | 56 |
G:=sub<GL(8,GF(73))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,72,0,0,1,0,0,0,0,72,72,0,0,0,0,0,0,2,0,0,72],[2,47,0,0,0,0,0,0,3,71,0,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,61,29,29,29,0,0,0,0,12,68,61,56,0,0,0,0,56,56,0,12,0,0,0,0,0,34,24,17],[71,1,0,0,0,0,0,0,70,2,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,29,12,61,44,0,0,0,0,61,5,12,17,0,0,0,0,0,49,56,61,0,0,0,0,24,24,0,56] >;
C3⋊C8⋊D4 in GAP, Magma, Sage, TeX
C_3\rtimes C_8\rtimes D_4
% in TeX
G:=Group("C3:C8:D4"); // GroupNames label
G:=SmallGroup(192,341);
// by ID
G=gap.SmallGroup(192,341);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,253,120,1094,135,570,297,136,6278]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^8=c^4=d^2=1,b*a*b^-1=c*a*c^-1=d*a*d=a^-1,c*b*c^-1=b^3,d*b*d=b^5,d*c*d=c^-1>;
// generators/relations
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