metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3⋊C8⋊1D4, C3⋊1(C8⋊D4), C4⋊C4.11D6, C4.D12⋊3C2, (C2×D4).28D6, C4.160(S3×D4), C6.Q16⋊8C2, (C2×C8).169D6, D4⋊C4⋊18S3, D6⋊3D4.5C2, C12.9(C4○D4), C12.110(C2×D4), C4.26(C4○D12), C6.17(C4⋊D4), C2.16(D8⋊S3), C6.34(C8⋊C22), C2.Dic12⋊26C2, (C2×Dic3).22D4, (C6×D4).41C22, (C22×S3).12D4, C22.178(S3×D4), C2.20(Dic3⋊D4), (C2×C12).220C23, (C2×C24).229C22, C2.12(D4.D6), C6.30(C8.C22), C4⋊Dic3.74C22, (C2×Dic6).58C22, (C2×D4.S3)⋊5C2, (C2×C8⋊S3)⋊17C2, (C2×C6).233(C2×D4), (C2×C3⋊C8).18C22, (S3×C2×C4).12C22, (C3×D4⋊C4)⋊29C2, (C3×C4⋊C4).21C22, (C2×C4).327(C22×S3), SmallGroup(192,339)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3⋊C8⋊1D4
G = < a,b,c,d | a3=b8=c4=d2=1, bab-1=cac-1=dad=a-1, cbc-1=b-1, dbd=b5, dcd=c-1 >
Subgroups: 376 in 120 conjugacy classes, 39 normal (37 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, S3, C6, C6, C8, C2×C4, C2×C4, D4, Q8, C23, Dic3, C12, C12, D6, C2×C6, C2×C6, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, M4(2), SD16, C22×C4, C2×D4, C2×D4, C2×Q8, C3⋊C8, C24, Dic6, C4×S3, C2×Dic3, C2×Dic3, C3⋊D4, C2×C12, C2×C12, C3×D4, C22×S3, C22×C6, D4⋊C4, Q8⋊C4, C2.D8, C4⋊D4, C22⋊Q8, C2×M4(2), C2×SD16, C8⋊S3, C2×C3⋊C8, C4⋊Dic3, C4⋊Dic3, D6⋊C4, D4.S3, C6.D4, C3×C4⋊C4, C2×C24, C2×Dic6, S3×C2×C4, C2×C3⋊D4, C6×D4, C8⋊D4, C6.Q16, C2.Dic12, C3×D4⋊C4, C4.D12, C2×C8⋊S3, C2×D4.S3, D6⋊3D4, C3⋊C8⋊1D4
Quotients: C1, C2, C22, S3, D4, C23, D6, C2×D4, C4○D4, C22×S3, C4⋊D4, C8⋊C22, C8.C22, C4○D12, S3×D4, C8⋊D4, Dic3⋊D4, D8⋊S3, D4.D6, C3⋊C8⋊1D4
Character table of C3⋊C8⋊1D4
| class | 1 | 2A | 2B | 2C | 2D | 2E | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 6A | 6B | 6C | 6D | 6E | 8A | 8B | 8C | 8D | 12A | 12B | 12C | 12D | 24A | 24B | 24C | 24D | |
| size | 1 | 1 | 1 | 1 | 8 | 12 | 2 | 2 | 2 | 8 | 12 | 24 | 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 | -2 | 0 | -1 | 2 | 2 | -2 | 0 | 0 | 0 | -1 | -1 | -1 | 1 | 1 | 2 | 2 | 0 | 0 | -1 | -1 | 1 | 1 | -1 | -1 | -1 | -1 | orthogonal lifted from D6 |
| ρ10 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ11 | 2 | 2 | 2 | 2 | 2 | 0 | -1 | 2 | 2 | -2 | 0 | 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 | -2 | 2 | -2 | -2 | 0 | 2 | 0 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ13 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ14 | 2 | 2 | 2 | 2 | 0 | 2 | 2 | -2 | -2 | 0 | -2 | 0 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ15 | 2 | 2 | 2 | 2 | -2 | 0 | -1 | 2 | 2 | 2 | 0 | 0 | 0 | -1 | -1 | -1 | 1 | 1 | -2 | -2 | 0 | 0 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | orthogonal lifted from D6 |
| ρ16 | 2 | 2 | 2 | 2 | 2 | 0 | -1 | 2 | 2 | 2 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ17 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | -2 | 2 | 0 | 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 | 2 | -2 | 2 | 0 | 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 | -1 | -2 | 2 | 0 | 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 | -1 | -2 | 2 | 0 | 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 | -1 | -2 | 2 | 0 | 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 | -1 | -2 | 2 | 0 | 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 | 4 | 0 | 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 |
| ρ24 | 4 | 4 | 4 | 4 | 0 | 0 | -2 | -4 | -4 | 0 | 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 |
| ρ25 | 4 | 4 | -4 | -4 | 0 | 0 | -2 | 4 | -4 | 0 | 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 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | -4 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C8.C22, Schur index 2 |
| ρ27 | 4 | -4 | -4 | 4 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -√6 | √6 | -√6 | √6 | symplectic lifted from D4.D6, Schur index 2 |
| ρ28 | 4 | -4 | -4 | 4 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | √6 | -√6 | √6 | -√6 | symplectic lifted from D4.D6, Schur index 2 |
| ρ29 | 4 | -4 | 4 | -4 | 0 | 0 | -2 | 0 | 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 | -2 | 0 | 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 57 76)(2 77 58)(3 59 78)(4 79 60)(5 61 80)(6 73 62)(7 63 74)(8 75 64)(9 48 65)(10 66 41)(11 42 67)(12 68 43)(13 44 69)(14 70 45)(15 46 71)(16 72 47)(17 84 40)(18 33 85)(19 86 34)(20 35 87)(21 88 36)(22 37 81)(23 82 38)(24 39 83)(25 92 54)(26 55 93)(27 94 56)(28 49 95)(29 96 50)(30 51 89)(31 90 52)(32 53 91)
(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 52 21 16)(2 51 22 15)(3 50 23 14)(4 49 24 13)(5 56 17 12)(6 55 18 11)(7 54 19 10)(8 53 20 9)(25 34 66 74)(26 33 67 73)(27 40 68 80)(28 39 69 79)(29 38 70 78)(30 37 71 77)(31 36 72 76)(32 35 65 75)(41 63 92 86)(42 62 93 85)(43 61 94 84)(44 60 95 83)(45 59 96 82)(46 58 89 81)(47 57 90 88)(48 64 91 87)
(2 6)(4 8)(9 49)(10 54)(11 51)(12 56)(13 53)(14 50)(15 55)(16 52)(18 22)(20 24)(25 41)(26 46)(27 43)(28 48)(29 45)(30 42)(31 47)(32 44)(33 81)(34 86)(35 83)(36 88)(37 85)(38 82)(39 87)(40 84)(57 76)(58 73)(59 78)(60 75)(61 80)(62 77)(63 74)(64 79)(65 95)(66 92)(67 89)(68 94)(69 91)(70 96)(71 93)(72 90)
G:=sub<Sym(96)| (1,57,76)(2,77,58)(3,59,78)(4,79,60)(5,61,80)(6,73,62)(7,63,74)(8,75,64)(9,48,65)(10,66,41)(11,42,67)(12,68,43)(13,44,69)(14,70,45)(15,46,71)(16,72,47)(17,84,40)(18,33,85)(19,86,34)(20,35,87)(21,88,36)(22,37,81)(23,82,38)(24,39,83)(25,92,54)(26,55,93)(27,94,56)(28,49,95)(29,96,50)(30,51,89)(31,90,52)(32,53,91), (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), (1,52,21,16)(2,51,22,15)(3,50,23,14)(4,49,24,13)(5,56,17,12)(6,55,18,11)(7,54,19,10)(8,53,20,9)(25,34,66,74)(26,33,67,73)(27,40,68,80)(28,39,69,79)(29,38,70,78)(30,37,71,77)(31,36,72,76)(32,35,65,75)(41,63,92,86)(42,62,93,85)(43,61,94,84)(44,60,95,83)(45,59,96,82)(46,58,89,81)(47,57,90,88)(48,64,91,87), (2,6)(4,8)(9,49)(10,54)(11,51)(12,56)(13,53)(14,50)(15,55)(16,52)(18,22)(20,24)(25,41)(26,46)(27,43)(28,48)(29,45)(30,42)(31,47)(32,44)(33,81)(34,86)(35,83)(36,88)(37,85)(38,82)(39,87)(40,84)(57,76)(58,73)(59,78)(60,75)(61,80)(62,77)(63,74)(64,79)(65,95)(66,92)(67,89)(68,94)(69,91)(70,96)(71,93)(72,90)>;
G:=Group( (1,57,76)(2,77,58)(3,59,78)(4,79,60)(5,61,80)(6,73,62)(7,63,74)(8,75,64)(9,48,65)(10,66,41)(11,42,67)(12,68,43)(13,44,69)(14,70,45)(15,46,71)(16,72,47)(17,84,40)(18,33,85)(19,86,34)(20,35,87)(21,88,36)(22,37,81)(23,82,38)(24,39,83)(25,92,54)(26,55,93)(27,94,56)(28,49,95)(29,96,50)(30,51,89)(31,90,52)(32,53,91), (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), (1,52,21,16)(2,51,22,15)(3,50,23,14)(4,49,24,13)(5,56,17,12)(6,55,18,11)(7,54,19,10)(8,53,20,9)(25,34,66,74)(26,33,67,73)(27,40,68,80)(28,39,69,79)(29,38,70,78)(30,37,71,77)(31,36,72,76)(32,35,65,75)(41,63,92,86)(42,62,93,85)(43,61,94,84)(44,60,95,83)(45,59,96,82)(46,58,89,81)(47,57,90,88)(48,64,91,87), (2,6)(4,8)(9,49)(10,54)(11,51)(12,56)(13,53)(14,50)(15,55)(16,52)(18,22)(20,24)(25,41)(26,46)(27,43)(28,48)(29,45)(30,42)(31,47)(32,44)(33,81)(34,86)(35,83)(36,88)(37,85)(38,82)(39,87)(40,84)(57,76)(58,73)(59,78)(60,75)(61,80)(62,77)(63,74)(64,79)(65,95)(66,92)(67,89)(68,94)(69,91)(70,96)(71,93)(72,90) );
G=PermutationGroup([[(1,57,76),(2,77,58),(3,59,78),(4,79,60),(5,61,80),(6,73,62),(7,63,74),(8,75,64),(9,48,65),(10,66,41),(11,42,67),(12,68,43),(13,44,69),(14,70,45),(15,46,71),(16,72,47),(17,84,40),(18,33,85),(19,86,34),(20,35,87),(21,88,36),(22,37,81),(23,82,38),(24,39,83),(25,92,54),(26,55,93),(27,94,56),(28,49,95),(29,96,50),(30,51,89),(31,90,52),(32,53,91)], [(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)], [(1,52,21,16),(2,51,22,15),(3,50,23,14),(4,49,24,13),(5,56,17,12),(6,55,18,11),(7,54,19,10),(8,53,20,9),(25,34,66,74),(26,33,67,73),(27,40,68,80),(28,39,69,79),(29,38,70,78),(30,37,71,77),(31,36,72,76),(32,35,65,75),(41,63,92,86),(42,62,93,85),(43,61,94,84),(44,60,95,83),(45,59,96,82),(46,58,89,81),(47,57,90,88),(48,64,91,87)], [(2,6),(4,8),(9,49),(10,54),(11,51),(12,56),(13,53),(14,50),(15,55),(16,52),(18,22),(20,24),(25,41),(26,46),(27,43),(28,48),(29,45),(30,42),(31,47),(32,44),(33,81),(34,86),(35,83),(36,88),(37,85),(38,82),(39,87),(40,84),(57,76),(58,73),(59,78),(60,75),(61,80),(62,77),(63,74),(64,79),(65,95),(66,92),(67,89),(68,94),(69,91),(70,96),(71,93),(72,90)]])
Matrix representation of C3⋊C8⋊1D4 ►in GL6(𝔽73)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 |
| 0 | 0 | 1 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 72 |
| 0 | 0 | 0 | 0 | 1 | 72 |
| 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 22 | 62 |
| 0 | 0 | 0 | 0 | 11 | 51 |
| 0 | 0 | 62 | 42 | 22 | 62 |
| 0 | 0 | 31 | 11 | 11 | 51 |
| 53 | 3 | 0 | 0 | 0 | 0 |
| 61 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 11 | 0 | 52 |
| 0 | 0 | 11 | 0 | 52 | 0 |
| 0 | 0 | 0 | 37 | 0 | 62 |
| 0 | 0 | 37 | 0 | 62 | 0 |
| 72 | 0 | 0 | 0 | 0 | 0 |
| 11 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(6,GF(73))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,72,72,0,0,0,0,0,0,0,1,0,0,0,0,72,72],[72,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,62,31,0,0,0,0,42,11,0,0,22,11,22,11,0,0,62,51,62,51],[53,61,0,0,0,0,3,20,0,0,0,0,0,0,0,11,0,37,0,0,11,0,37,0,0,0,0,52,0,62,0,0,52,0,62,0],[72,11,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0] >;
C3⋊C8⋊1D4 in GAP, Magma, Sage, TeX
C_3\rtimes C_8\rtimes_1D_4
% in TeX
G:=Group("C3:C8:1D4"); // GroupNames label
G:=SmallGroup(192,339);
// by ID
G=gap.SmallGroup(192,339);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,253,1094,135,100,570,297,136,6278]);
// 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^-1,d*b*d=b^5,d*c*d=c^-1>;
// generators/relations
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