metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3⋊C8⋊6D4, C3⋊5(C8⋊D4), C4⋊C4.68D6, C22⋊Q8⋊4S3, (C2×C12).78D4, C4.175(S3×D4), (C2×Q8).54D6, C6.D8⋊40C2, C6.Q16⋊40C2, C12.155(C2×D4), (C22×C6).95D4, C12⋊7D4.13C2, Q8⋊2Dic3⋊16C2, C6.98(C4⋊D4), (C22×C4).145D6, C12.191(C4○D4), (C6×Q8).48C22, C2.16(D4⋊D6), C4.64(D4⋊2S3), C6.117(C8⋊C22), (C2×C12).368C23, C6.91(C8.C22), C23.35(C3⋊D4), (C2×D12).100C22, C4⋊Dic3.147C22, C2.19(C23.14D6), C2.12(Q8.11D6), (C22×C12).172C22, (C3×C22⋊Q8)⋊4C2, (C2×C6).499(C2×D4), (C2×Q8⋊2S3)⋊11C2, (C2×C4).56(C3⋊D4), (C2×C3⋊C8).116C22, (C2×C4.Dic3)⋊13C2, (C3×C4⋊C4).115C22, (C2×C4).468(C22×S3), C22.174(C2×C3⋊D4), SmallGroup(192,608)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3⋊C8⋊6D4
G = < a,b,c,d | a3=b8=c4=d2=1, bab-1=cac-1=a-1, ad=da, cbc-1=b-1, dbd=b5, dcd=c-1 >
Subgroups: 368 in 120 conjugacy classes, 41 normal (39 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, S3, C6, C6, C8, C2×C4, C2×C4, D4, Q8, C23, C23, Dic3, C12, C12, D6, C2×C6, C2×C6, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, M4(2), SD16, C22×C4, C2×D4, C2×Q8, C3⋊C8, C3⋊C8, D12, C2×Dic3, C3⋊D4, C2×C12, C2×C12, C3×Q8, C22×S3, C22×C6, D4⋊C4, Q8⋊C4, C2.D8, C4⋊D4, C22⋊Q8, C2×M4(2), C2×SD16, C2×C3⋊C8, C4.Dic3, C4⋊Dic3, D6⋊C4, Q8⋊2S3, C3×C22⋊C4, C3×C4⋊C4, C3×C4⋊C4, C2×D12, C2×C3⋊D4, C22×C12, C6×Q8, C8⋊D4, C6.Q16, C6.D8, Q8⋊2Dic3, C2×C4.Dic3, C12⋊7D4, C2×Q8⋊2S3, C3×C22⋊Q8, C3⋊C8⋊6D4
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, C23.14D6, Q8.11D6, D4⋊D6, C3⋊C8⋊6D4
Character table of C3⋊C8⋊6D4
| 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 | 12E | 12F | 12G | 12H | |
| size | 1 | 1 | 1 | 1 | 4 | 24 | 2 | 2 | 2 | 4 | 8 | 8 | 24 | 2 | 2 | 2 | 4 | 4 | 12 | 12 | 12 | 12 | 4 | 4 | 4 | 4 | 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 | 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 | -2 | 2 | 0 | -1 | -1 | -1 | 1 | 1 | 0 | 0 | 0 | 0 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 | orthogonal lifted from D6 |
| ρ10 | 2 | 2 | 2 | 2 | 2 | 0 | -1 | 2 | 2 | 2 | -2 | -2 | 0 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | orthogonal lifted from D6 |
| ρ11 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | 0 | 0 | 0 | -2 | 2 | 0 | 2 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ12 | 2 | 2 | 2 | 2 | -2 | 0 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 2 | 2 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | -2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ13 | 2 | 2 | 2 | 2 | 2 | 0 | -1 | 2 | 2 | 2 | 2 | 2 | 0 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ14 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | 0 | 0 | 0 | 2 | -2 | 0 | 2 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ15 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | -2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ16 | 2 | 2 | 2 | 2 | -2 | 0 | -1 | 2 | 2 | -2 | 2 | -2 | 0 | -1 | -1 | -1 | 1 | 1 | 0 | 0 | 0 | 0 | -1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | orthogonal lifted from D6 |
| ρ17 | 2 | 2 | 2 | 2 | -2 | 0 | -1 | -2 | -2 | 2 | 0 | 0 | 0 | -1 | -1 | -1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | -1 | 1 | -1 | -√-3 | -√-3 | √-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 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | √-3 | -√-3 | √-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 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | -√-3 | √-3 | -√-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 | 0 | 0 | 0 | 0 | 1 | -1 | 1 | -1 | √-3 | √-3 | -√-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 | -2i | 0 | 0 | 2i | -2 | 0 | 2 | 0 | 0 | 0 | 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 | 2i | 0 | 0 | -2i | -2 | 0 | 2 | 0 | 0 | 0 | 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 | -2 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from S3×D4 |
| ρ25 | 4 | -4 | 4 | -4 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2√3 | 0 | 2√3 | 0 | 0 | 0 | 0 | orthogonal lifted from D4⋊D6 |
| ρ26 | 4 | -4 | 4 | -4 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2√3 | 0 | -2√3 | 0 | 0 | 0 | 0 | orthogonal lifted from D4⋊D6 |
| ρ27 | 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 |
| ρ28 | 4 | 4 | -4 | -4 | 0 | 0 | -2 | 4 | -4 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from D4⋊2S3, 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 Q8.11D6 |
| 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 Q8.11D6 |
►On 96 points
Generators in S96
(1 86 57)(2 58 87)(3 88 59)(4 60 81)(5 82 61)(6 62 83)(7 84 63)(8 64 85)(9 50 29)(10 30 51)(11 52 31)(12 32 53)(13 54 25)(14 26 55)(15 56 27)(16 28 49)(17 65 74)(18 75 66)(19 67 76)(20 77 68)(21 69 78)(22 79 70)(23 71 80)(24 73 72)(33 43 92)(34 93 44)(35 45 94)(36 95 46)(37 47 96)(38 89 48)(39 41 90)(40 91 42)
(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 94 70 9)(2 93 71 16)(3 92 72 15)(4 91 65 14)(5 90 66 13)(6 89 67 12)(7 96 68 11)(8 95 69 10)(17 26 81 42)(18 25 82 41)(19 32 83 48)(20 31 84 47)(21 30 85 46)(22 29 86 45)(23 28 87 44)(24 27 88 43)(33 73 56 59)(34 80 49 58)(35 79 50 57)(36 78 51 64)(37 77 52 63)(38 76 53 62)(39 75 54 61)(40 74 55 60)
(1 94)(2 91)(3 96)(4 93)(5 90)(6 95)(7 92)(8 89)(9 70)(10 67)(11 72)(12 69)(13 66)(14 71)(15 68)(16 65)(17 49)(18 54)(19 51)(20 56)(21 53)(22 50)(23 55)(24 52)(25 75)(26 80)(27 77)(28 74)(29 79)(30 76)(31 73)(32 78)(33 84)(34 81)(35 86)(36 83)(37 88)(38 85)(39 82)(40 87)(41 61)(42 58)(43 63)(44 60)(45 57)(46 62)(47 59)(48 64)
G:=sub<Sym(96)| (1,86,57)(2,58,87)(3,88,59)(4,60,81)(5,82,61)(6,62,83)(7,84,63)(8,64,85)(9,50,29)(10,30,51)(11,52,31)(12,32,53)(13,54,25)(14,26,55)(15,56,27)(16,28,49)(17,65,74)(18,75,66)(19,67,76)(20,77,68)(21,69,78)(22,79,70)(23,71,80)(24,73,72)(33,43,92)(34,93,44)(35,45,94)(36,95,46)(37,47,96)(38,89,48)(39,41,90)(40,91,42), (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), (1,94,70,9)(2,93,71,16)(3,92,72,15)(4,91,65,14)(5,90,66,13)(6,89,67,12)(7,96,68,11)(8,95,69,10)(17,26,81,42)(18,25,82,41)(19,32,83,48)(20,31,84,47)(21,30,85,46)(22,29,86,45)(23,28,87,44)(24,27,88,43)(33,73,56,59)(34,80,49,58)(35,79,50,57)(36,78,51,64)(37,77,52,63)(38,76,53,62)(39,75,54,61)(40,74,55,60), (1,94)(2,91)(3,96)(4,93)(5,90)(6,95)(7,92)(8,89)(9,70)(10,67)(11,72)(12,69)(13,66)(14,71)(15,68)(16,65)(17,49)(18,54)(19,51)(20,56)(21,53)(22,50)(23,55)(24,52)(25,75)(26,80)(27,77)(28,74)(29,79)(30,76)(31,73)(32,78)(33,84)(34,81)(35,86)(36,83)(37,88)(38,85)(39,82)(40,87)(41,61)(42,58)(43,63)(44,60)(45,57)(46,62)(47,59)(48,64)>;
G:=Group( (1,86,57)(2,58,87)(3,88,59)(4,60,81)(5,82,61)(6,62,83)(7,84,63)(8,64,85)(9,50,29)(10,30,51)(11,52,31)(12,32,53)(13,54,25)(14,26,55)(15,56,27)(16,28,49)(17,65,74)(18,75,66)(19,67,76)(20,77,68)(21,69,78)(22,79,70)(23,71,80)(24,73,72)(33,43,92)(34,93,44)(35,45,94)(36,95,46)(37,47,96)(38,89,48)(39,41,90)(40,91,42), (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), (1,94,70,9)(2,93,71,16)(3,92,72,15)(4,91,65,14)(5,90,66,13)(6,89,67,12)(7,96,68,11)(8,95,69,10)(17,26,81,42)(18,25,82,41)(19,32,83,48)(20,31,84,47)(21,30,85,46)(22,29,86,45)(23,28,87,44)(24,27,88,43)(33,73,56,59)(34,80,49,58)(35,79,50,57)(36,78,51,64)(37,77,52,63)(38,76,53,62)(39,75,54,61)(40,74,55,60), (1,94)(2,91)(3,96)(4,93)(5,90)(6,95)(7,92)(8,89)(9,70)(10,67)(11,72)(12,69)(13,66)(14,71)(15,68)(16,65)(17,49)(18,54)(19,51)(20,56)(21,53)(22,50)(23,55)(24,52)(25,75)(26,80)(27,77)(28,74)(29,79)(30,76)(31,73)(32,78)(33,84)(34,81)(35,86)(36,83)(37,88)(38,85)(39,82)(40,87)(41,61)(42,58)(43,63)(44,60)(45,57)(46,62)(47,59)(48,64) );
G=PermutationGroup([[(1,86,57),(2,58,87),(3,88,59),(4,60,81),(5,82,61),(6,62,83),(7,84,63),(8,64,85),(9,50,29),(10,30,51),(11,52,31),(12,32,53),(13,54,25),(14,26,55),(15,56,27),(16,28,49),(17,65,74),(18,75,66),(19,67,76),(20,77,68),(21,69,78),(22,79,70),(23,71,80),(24,73,72),(33,43,92),(34,93,44),(35,45,94),(36,95,46),(37,47,96),(38,89,48),(39,41,90),(40,91,42)], [(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)], [(1,94,70,9),(2,93,71,16),(3,92,72,15),(4,91,65,14),(5,90,66,13),(6,89,67,12),(7,96,68,11),(8,95,69,10),(17,26,81,42),(18,25,82,41),(19,32,83,48),(20,31,84,47),(21,30,85,46),(22,29,86,45),(23,28,87,44),(24,27,88,43),(33,73,56,59),(34,80,49,58),(35,79,50,57),(36,78,51,64),(37,77,52,63),(38,76,53,62),(39,75,54,61),(40,74,55,60)], [(1,94),(2,91),(3,96),(4,93),(5,90),(6,95),(7,92),(8,89),(9,70),(10,67),(11,72),(12,69),(13,66),(14,71),(15,68),(16,65),(17,49),(18,54),(19,51),(20,56),(21,53),(22,50),(23,55),(24,52),(25,75),(26,80),(27,77),(28,74),(29,79),(30,76),(31,73),(32,78),(33,84),(34,81),(35,86),(36,83),(37,88),(38,85),(39,82),(40,87),(41,61),(42,58),(43,63),(44,60),(45,57),(46,62),(47,59),(48,64)]])
Matrix representation of C3⋊C8⋊6D4 ►in GL8(𝔽73)
| 0 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 72 | 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 | 72 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 72 | 72 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
| 72 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 67 | 0 | 6 | 0 |
| 0 | 0 | 0 | 0 | 6 | 6 | 67 | 67 |
| 0 | 0 | 0 | 0 | 67 | 0 | 67 | 0 |
| 0 | 0 | 0 | 0 | 6 | 6 | 6 | 6 |
| 46 | 50 | 7 | 33 | 0 | 0 | 0 | 0 |
| 23 | 27 | 40 | 66 | 0 | 0 | 0 | 0 |
| 66 | 40 | 27 | 23 | 0 | 0 | 0 | 0 |
| 33 | 7 | 50 | 46 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 30 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 30 | 43 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 43 | 13 |
| 0 | 0 | 0 | 0 | 0 | 0 | 43 | 30 |
| 50 | 46 | 33 | 7 | 0 | 0 | 0 | 0 |
| 27 | 23 | 66 | 40 | 0 | 0 | 0 | 0 |
| 40 | 66 | 23 | 27 | 0 | 0 | 0 | 0 |
| 7 | 33 | 46 | 50 | 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 | 43 | 13 |
| 0 | 0 | 0 | 0 | 0 | 0 | 60 | 30 |
G:=sub<GL(8,GF(73))| [0,1,0,0,0,0,0,0,72,72,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72,0,0,0,0,0,0,0,0,72,1,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,72,1,0,0,0,0,0,0,72,0],[0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,0,0,67,6,67,6,0,0,0,0,0,6,0,6,0,0,0,0,6,67,67,6,0,0,0,0,0,67,0,6],[46,23,66,33,0,0,0,0,50,27,40,7,0,0,0,0,7,40,27,50,0,0,0,0,33,66,23,46,0,0,0,0,0,0,0,0,30,30,0,0,0,0,0,0,60,43,0,0,0,0,0,0,0,0,43,43,0,0,0,0,0,0,13,30],[50,27,40,7,0,0,0,0,46,23,66,33,0,0,0,0,33,66,23,46,0,0,0,0,7,40,27,50,0,0,0,0,0,0,0,0,43,60,0,0,0,0,0,0,13,30,0,0,0,0,0,0,0,0,43,60,0,0,0,0,0,0,13,30] >;
C3⋊C8⋊6D4 in GAP, Magma, Sage, TeX
C_3\rtimes C_8\rtimes_6D_4
% in TeX
G:=Group("C3:C8:6D4"); // GroupNames label
G:=SmallGroup(192,608);
// by ID
G=gap.SmallGroup(192,608);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,253,254,555,184,1123,297,136,6278]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^8=c^4=d^2=1,b*a*b^-1=c*a*c^-1=a^-1,a*d=d*a,c*b*c^-1=b^-1,d*b*d=b^5,d*c*d=c^-1>;
// generators/relations
Export