metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3⋊C8⋊5D4, C3⋊4(C8⋊D4), C4⋊C4.62D6, (C2×D4).42D6, (C2×C12).74D4, C4.173(S3×D4), C4⋊D4.7S3, C12.151(C2×D4), C6.Q16⋊37C2, (C22×C6).88D4, D4⋊Dic3⋊18C2, C6.SD16⋊36C2, C6.96(C4⋊D4), C6.92(C8⋊C22), (C6×D4).58C22, (C22×C4).139D6, C12.186(C4○D4), C4.62(D4⋊2S3), C12.48D4⋊25C2, (C2×C12).361C23, C23.32(C3⋊D4), C2.13(Q8.14D6), C2.13(D12⋊6C22), C6.115(C8.C22), C4⋊Dic3.145C22, C2.17(C23.14D6), (C22×C12).165C22, (C2×Dic6).104C22, (C2×D4.S3)⋊11C2, (C3×C4⋊D4).6C2, (C2×C6).492(C2×D4), (C2×C4).52(C3⋊D4), (C2×C3⋊C8).111C22, (C2×C4.Dic3)⋊12C2, (C3×C4⋊C4).109C22, (C2×C4).461(C22×S3), C22.167(C2×C3⋊D4), SmallGroup(192,601)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3⋊C8⋊5D4
G = < a,b,c,d | a3=b8=c4=d2=1, bab-1=a-1, ac=ca, ad=da, cbc-1=b-1, dbd=b5, dcd=c-1 >
Subgroups: 320 in 120 conjugacy classes, 41 normal (39 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, C6, C6, C8, C2×C4, C2×C4, D4, Q8, C23, C23, Dic3, C12, C12, C2×C6, C2×C6, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, M4(2), SD16, C22×C4, C2×D4, C2×D4, C2×Q8, C3⋊C8, C3⋊C8, Dic6, C2×Dic3, C2×C12, C2×C12, C3×D4, C22×C6, C22×C6, D4⋊C4, Q8⋊C4, C2.D8, C4⋊D4, C22⋊Q8, C2×M4(2), C2×SD16, C2×C3⋊C8, C4.Dic3, Dic3⋊C4, C4⋊Dic3, D4.S3, C6.D4, C3×C22⋊C4, C3×C4⋊C4, C2×Dic6, C22×C12, C6×D4, C6×D4, C8⋊D4, C6.Q16, C6.SD16, D4⋊Dic3, C2×C4.Dic3, C12.48D4, C2×D4.S3, C3×C4⋊D4, C3⋊C8⋊5D4
Quotients: C1, C2, C22, S3, D4, C23, D6, C2×D4, C4○D4, C3⋊D4, C22×S3, C4⋊D4, C8⋊C22, C8.C22, S3×D4, D4⋊2S3, C2×C3⋊D4, C8⋊D4, D12⋊6C22, C23.14D6, Q8.14D6, C3⋊C8⋊5D4
Character table of C3⋊C8⋊5D4
| class | 1 | 2A | 2B | 2C | 2D | 2E | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 6A | 6B | 6C | 6D | 6E | 6F | 6G | 8A | 8B | 8C | 8D | 12A | 12B | 12C | 12D | 12E | 12F | |
| size | 1 | 1 | 1 | 1 | 4 | 8 | 2 | 2 | 2 | 4 | 8 | 24 | 24 | 2 | 2 | 2 | 4 | 4 | 8 | 8 | 12 | 12 | 12 | 12 | 4 | 4 | 4 | 4 | 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 | 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 | 2 | -1 | 2 | 2 | -2 | -2 | 0 | 0 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | 0 | 0 | 0 | 0 | -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 | 0 | -2 | 0 | 2 | 2 | 0 | 0 | -2 | 0 | 0 | orthogonal lifted from D4 |
| ρ11 | 2 | 2 | 2 | 2 | 2 | -2 | -1 | 2 | 2 | 2 | -2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | 1 | 1 | orthogonal lifted from D6 |
| ρ12 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | -2 | -2 | 0 | 0 | orthogonal lifted from D4 |
| ρ13 | 2 | 2 | 2 | 2 | -2 | 0 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 2 | 2 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | -2 | 0 | 0 | orthogonal lifted from D4 |
| ρ14 | 2 | 2 | 2 | 2 | -2 | -2 | -1 | 2 | 2 | -2 | 2 | 0 | 0 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | -1 | 1 | 1 | -1 | -1 | -1 | orthogonal lifted from D6 |
| ρ15 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | -2 | 2 | 0 | 0 | -2 | 0 | 0 | orthogonal lifted from D4 |
| ρ16 | 2 | 2 | 2 | 2 | 2 | 2 | -1 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ17 | 2 | 2 | 2 | 2 | 2 | 0 | -1 | -2 | -2 | -2 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | √-3 | -√-3 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | -√-3 | √-3 | complex lifted from C3⋊D4 |
| ρ18 | 2 | 2 | 2 | 2 | -2 | 0 | -1 | -2 | -2 | 2 | 0 | 0 | 0 | -1 | -1 | -1 | 1 | 1 | -√-3 | √-3 | 0 | 0 | 0 | 0 | 1 | -1 | -1 | 1 | -√-3 | √-3 | complex lifted from C3⋊D4 |
| ρ19 | 2 | 2 | 2 | 2 | -2 | 0 | -1 | -2 | -2 | 2 | 0 | 0 | 0 | -1 | -1 | -1 | 1 | 1 | √-3 | -√-3 | 0 | 0 | 0 | 0 | 1 | -1 | -1 | 1 | √-3 | -√-3 | complex lifted from C3⋊D4 |
| ρ20 | 2 | 2 | 2 | 2 | 2 | 0 | -1 | -2 | -2 | -2 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -√-3 | √-3 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | √-3 | -√-3 | complex lifted from C3⋊D4 |
| ρ21 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | -2i | 0 | 2i | 0 | -2 | 0 | 0 | 2 | 0 | 0 | complex lifted from C4○D4 |
| ρ22 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | 2i | 0 | -2i | 0 | -2 | 0 | 0 | 2 | 0 | 0 | complex lifted from C4○D4 |
| 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 | 0 | 0 | -2 | 0 | 0 | 2 | 0 | 0 | orthogonal lifted from S3×D4 |
| ρ25 | 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 |
| ρ26 | 4 | 4 | -4 | -4 | 0 | 0 | -2 | 4 | -4 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | -2 | 0 | 0 | symplectic lifted from D4⋊2S3, 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 | -2√3 | 2√3 | 0 | 0 | 0 | symplectic lifted from Q8.14D6, 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 | 2√3 | -2√3 | 0 | 0 | 0 | symplectic lifted from Q8.14D6, Schur index 2 |
| ρ29 | 4 | -4 | -4 | 4 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | 2√-3 | -2√-3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from D12⋊6C22 |
| ρ30 | 4 | -4 | -4 | 4 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | -2√-3 | 2√-3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from D12⋊6C22 |
►On 96 points
Generators in S96
(1 41 50)(2 51 42)(3 43 52)(4 53 44)(5 45 54)(6 55 46)(7 47 56)(8 49 48)(9 29 86)(10 87 30)(11 31 88)(12 81 32)(13 25 82)(14 83 26)(15 27 84)(16 85 28)(17 92 77)(18 78 93)(19 94 79)(20 80 95)(21 96 73)(22 74 89)(23 90 75)(24 76 91)(33 63 66)(34 67 64)(35 57 68)(36 69 58)(37 59 70)(38 71 60)(39 61 72)(40 65 62)
(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 37 95 15)(2 36 96 14)(3 35 89 13)(4 34 90 12)(5 33 91 11)(6 40 92 10)(7 39 93 9)(8 38 94 16)(17 30 46 62)(18 29 47 61)(19 28 48 60)(20 27 41 59)(21 26 42 58)(22 25 43 57)(23 32 44 64)(24 31 45 63)(49 71 79 85)(50 70 80 84)(51 69 73 83)(52 68 74 82)(53 67 75 81)(54 66 76 88)(55 65 77 87)(56 72 78 86)
(1 15)(2 12)(3 9)(4 14)(5 11)(6 16)(7 13)(8 10)(17 60)(18 57)(19 62)(20 59)(21 64)(22 61)(23 58)(24 63)(25 47)(26 44)(27 41)(28 46)(29 43)(30 48)(31 45)(32 42)(33 91)(34 96)(35 93)(36 90)(37 95)(38 92)(39 89)(40 94)(49 87)(50 84)(51 81)(52 86)(53 83)(54 88)(55 85)(56 82)(65 79)(66 76)(67 73)(68 78)(69 75)(70 80)(71 77)(72 74)
G:=sub<Sym(96)| (1,41,50)(2,51,42)(3,43,52)(4,53,44)(5,45,54)(6,55,46)(7,47,56)(8,49,48)(9,29,86)(10,87,30)(11,31,88)(12,81,32)(13,25,82)(14,83,26)(15,27,84)(16,85,28)(17,92,77)(18,78,93)(19,94,79)(20,80,95)(21,96,73)(22,74,89)(23,90,75)(24,76,91)(33,63,66)(34,67,64)(35,57,68)(36,69,58)(37,59,70)(38,71,60)(39,61,72)(40,65,62), (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), (1,37,95,15)(2,36,96,14)(3,35,89,13)(4,34,90,12)(5,33,91,11)(6,40,92,10)(7,39,93,9)(8,38,94,16)(17,30,46,62)(18,29,47,61)(19,28,48,60)(20,27,41,59)(21,26,42,58)(22,25,43,57)(23,32,44,64)(24,31,45,63)(49,71,79,85)(50,70,80,84)(51,69,73,83)(52,68,74,82)(53,67,75,81)(54,66,76,88)(55,65,77,87)(56,72,78,86), (1,15)(2,12)(3,9)(4,14)(5,11)(6,16)(7,13)(8,10)(17,60)(18,57)(19,62)(20,59)(21,64)(22,61)(23,58)(24,63)(25,47)(26,44)(27,41)(28,46)(29,43)(30,48)(31,45)(32,42)(33,91)(34,96)(35,93)(36,90)(37,95)(38,92)(39,89)(40,94)(49,87)(50,84)(51,81)(52,86)(53,83)(54,88)(55,85)(56,82)(65,79)(66,76)(67,73)(68,78)(69,75)(70,80)(71,77)(72,74)>;
G:=Group( (1,41,50)(2,51,42)(3,43,52)(4,53,44)(5,45,54)(6,55,46)(7,47,56)(8,49,48)(9,29,86)(10,87,30)(11,31,88)(12,81,32)(13,25,82)(14,83,26)(15,27,84)(16,85,28)(17,92,77)(18,78,93)(19,94,79)(20,80,95)(21,96,73)(22,74,89)(23,90,75)(24,76,91)(33,63,66)(34,67,64)(35,57,68)(36,69,58)(37,59,70)(38,71,60)(39,61,72)(40,65,62), (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), (1,37,95,15)(2,36,96,14)(3,35,89,13)(4,34,90,12)(5,33,91,11)(6,40,92,10)(7,39,93,9)(8,38,94,16)(17,30,46,62)(18,29,47,61)(19,28,48,60)(20,27,41,59)(21,26,42,58)(22,25,43,57)(23,32,44,64)(24,31,45,63)(49,71,79,85)(50,70,80,84)(51,69,73,83)(52,68,74,82)(53,67,75,81)(54,66,76,88)(55,65,77,87)(56,72,78,86), (1,15)(2,12)(3,9)(4,14)(5,11)(6,16)(7,13)(8,10)(17,60)(18,57)(19,62)(20,59)(21,64)(22,61)(23,58)(24,63)(25,47)(26,44)(27,41)(28,46)(29,43)(30,48)(31,45)(32,42)(33,91)(34,96)(35,93)(36,90)(37,95)(38,92)(39,89)(40,94)(49,87)(50,84)(51,81)(52,86)(53,83)(54,88)(55,85)(56,82)(65,79)(66,76)(67,73)(68,78)(69,75)(70,80)(71,77)(72,74) );
G=PermutationGroup([[(1,41,50),(2,51,42),(3,43,52),(4,53,44),(5,45,54),(6,55,46),(7,47,56),(8,49,48),(9,29,86),(10,87,30),(11,31,88),(12,81,32),(13,25,82),(14,83,26),(15,27,84),(16,85,28),(17,92,77),(18,78,93),(19,94,79),(20,80,95),(21,96,73),(22,74,89),(23,90,75),(24,76,91),(33,63,66),(34,67,64),(35,57,68),(36,69,58),(37,59,70),(38,71,60),(39,61,72),(40,65,62)], [(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)], [(1,37,95,15),(2,36,96,14),(3,35,89,13),(4,34,90,12),(5,33,91,11),(6,40,92,10),(7,39,93,9),(8,38,94,16),(17,30,46,62),(18,29,47,61),(19,28,48,60),(20,27,41,59),(21,26,42,58),(22,25,43,57),(23,32,44,64),(24,31,45,63),(49,71,79,85),(50,70,80,84),(51,69,73,83),(52,68,74,82),(53,67,75,81),(54,66,76,88),(55,65,77,87),(56,72,78,86)], [(1,15),(2,12),(3,9),(4,14),(5,11),(6,16),(7,13),(8,10),(17,60),(18,57),(19,62),(20,59),(21,64),(22,61),(23,58),(24,63),(25,47),(26,44),(27,41),(28,46),(29,43),(30,48),(31,45),(32,42),(33,91),(34,96),(35,93),(36,90),(37,95),(38,92),(39,89),(40,94),(49,87),(50,84),(51,81),(52,86),(53,83),(54,88),(55,85),(56,82),(65,79),(66,76),(67,73),(68,78),(69,75),(70,80),(71,77),(72,74)]])
Matrix representation of C3⋊C8⋊5D4 ►in GL8(𝔽73)
| 0 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 64 | 0 | 0 | 0 | 0 | 0 |
| 8 | 1 | 2 | 8 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 72 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 72 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 72 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
| 28 | 0 | 72 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 4 | 4 |
| 0 | 0 | 0 | 0 | 0 | 0 | 4 | 65 |
| 0 | 0 | 0 | 0 | 61 | 67 | 0 | 61 |
| 0 | 0 | 0 | 0 | 67 | 6 | 61 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 65 | 72 | 71 | 65 | 0 | 0 | 0 | 0 |
| 8 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 72 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 43 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 60 | 30 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 17 | 43 | 60 |
| 0 | 0 | 0 | 0 | 0 | 17 | 13 | 30 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 65 | 72 | 71 | 65 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 43 | 13 | 0 | 0 |
| 0 | 0 | 0 | 0 | 60 | 30 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 30 | 13 |
| 0 | 0 | 0 | 0 | 0 | 0 | 60 | 43 |
G:=sub<GL(8,GF(73))| [0,1,0,8,0,0,0,0,72,72,0,1,0,0,0,0,0,0,64,2,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,72,1,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72],[1,1,28,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,28,1,0,0,0,0,0,0,0,0,0,0,61,67,0,0,0,0,0,0,67,6,0,0,0,0,4,4,0,61,0,0,0,0,4,65,61,0],[0,65,8,72,0,0,0,0,0,72,1,0,0,0,0,0,0,71,1,0,0,0,0,0,1,65,0,0,0,0,0,0,0,0,0,0,43,60,17,0,0,0,0,0,13,30,17,17,0,0,0,0,0,0,43,13,0,0,0,0,0,0,60,30],[0,65,0,1,0,0,0,0,0,72,0,0,0,0,0,0,0,71,1,0,0,0,0,0,1,65,0,0,0,0,0,0,0,0,0,0,43,60,0,0,0,0,0,0,13,30,0,0,0,0,0,0,0,0,30,60,0,0,0,0,0,0,13,43] >;
C3⋊C8⋊5D4 in GAP, Magma, Sage, TeX
C_3\rtimes C_8\rtimes_5D_4
% in TeX
G:=Group("C3:C8:5D4"); // GroupNames label
G:=SmallGroup(192,601);
// by ID
G=gap.SmallGroup(192,601);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,224,253,254,555,1123,297,136,6278]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^8=c^4=d^2=1,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,d*b*d=b^5,d*c*d=c^-1>;
// generators/relations
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