metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3⋊C8.1D4, C4⋊C4.30D6, (C2×C8).178D6, C4.169(S3×D4), C3⋊1(C8.D4), (C2×Q8).46D6, Q8⋊C4⋊19S3, C12.127(C2×D4), C4.D12.3C2, D6⋊3Q8.6C2, C4.35(C4○D12), C12.22(C4○D4), C6.26(C4⋊D4), C12.Q8⋊13C2, C2.Dic12⋊30C2, (C2×Dic3).34D4, (C22×S3).22D4, C22.206(S3×D4), (C6×Q8).39C22, C2.29(Dic3⋊D4), (C2×C12).256C23, (C2×C24).246C22, C2.18(Q16⋊S3), C2.19(D4.D6), C6.64(C8.C22), C4⋊Dic3.100C22, (C2×Dic6).74C22, (C2×C3⋊Q16)⋊6C2, (C2×C8⋊S3).7C2, (C2×C6).269(C2×D4), (C2×C3⋊C8).46C22, (S3×C2×C4).28C22, (C3×Q8⋊C4)⋊29C2, (C3×C4⋊C4).57C22, (C2×C4).363(C22×S3), SmallGroup(192,375)
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=dad=a-1, ac=ca, cbc-1=b3, dbd=b5, dcd=b4c-1 >
Subgroups: 312 in 110 conjugacy classes, 39 normal (37 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, S3, C6, C8, C2×C4, C2×C4, Q8, C23, Dic3, C12, C12, D6, C2×C6, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, M4(2), Q16, C22×C4, C2×Q8, C2×Q8, C3⋊C8, C24, Dic6, C4×S3, C2×Dic3, C2×Dic3, C2×C12, C2×C12, C3×Q8, C22×S3, Q8⋊C4, Q8⋊C4, C4.Q8, C22⋊Q8, C2×M4(2), C2×Q16, C8⋊S3, C2×C3⋊C8, Dic3⋊C4, C4⋊Dic3, C4⋊Dic3, D6⋊C4, C3⋊Q16, C3×C4⋊C4, C2×C24, C2×Dic6, S3×C2×C4, C6×Q8, C8.D4, C12.Q8, C2.Dic12, C3×Q8⋊C4, C4.D12, C2×C8⋊S3, C2×C3⋊Q16, D6⋊3Q8, 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.D4, Dic3⋊D4, D4.D6, Q16⋊S3, C3⋊C8.D4
Character table of C3⋊C8.D4
| class | 1 | 2A | 2B | 2C | 2D | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 6A | 6B | 6C | 8A | 8B | 8C | 8D | 12A | 12B | 12C | 12D | 12E | 12F | 24A | 24B | 24C | 24D | |
| size | 1 | 1 | 1 | 1 | 12 | 2 | 2 | 2 | 8 | 8 | 12 | 24 | 24 | 2 | 2 | 2 | 4 | 4 | 12 | 12 | 4 | 4 | 8 | 8 | 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 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 0 | 0 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ10 | 2 | 2 | 2 | 2 | 0 | -1 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | -1 | -1 | -1 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ11 | 2 | -2 | -2 | 2 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 0 | 0 | -2 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ12 | 2 | 2 | 2 | 2 | 0 | -1 | 2 | 2 | -2 | 2 | 0 | 0 | 0 | -1 | -1 | -1 | -2 | -2 | 0 | 0 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | orthogonal lifted from D6 |
| ρ13 | 2 | 2 | 2 | 2 | 2 | 2 | -2 | -2 | 0 | 0 | -2 | 0 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ14 | 2 | 2 | 2 | 2 | -2 | 2 | -2 | -2 | 0 | 0 | 2 | 0 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ15 | 2 | 2 | 2 | 2 | 0 | -1 | 2 | 2 | -2 | -2 | 0 | 0 | 0 | -1 | -1 | -1 | 2 | 2 | 0 | 0 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | orthogonal lifted from D6 |
| ρ16 | 2 | 2 | 2 | 2 | 0 | -1 | 2 | 2 | 2 | -2 | 0 | 0 | 0 | -1 | -1 | -1 | -2 | -2 | 0 | 0 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | orthogonal lifted from D6 |
| ρ17 | 2 | -2 | -2 | 2 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 2i | -2i | 0 | 0 | -2 | 2 | 0 | 0 | 0 | 0 | -2i | 2i | 2i | -2i | complex lifted from C4○D4 |
| ρ18 | 2 | -2 | -2 | 2 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | -2i | 2i | 0 | 0 | -2 | 2 | 0 | 0 | 0 | 0 | 2i | -2i | -2i | 2i | complex lifted from C4○D4 |
| ρ19 | 2 | -2 | -2 | 2 | 0 | -1 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | 1 | -2i | 2i | 0 | 0 | 1 | -1 | √-3 | -√-3 | -√3 | √3 | -i | i | i | -i | complex lifted from C4○D12 |
| ρ20 | 2 | -2 | -2 | 2 | 0 | -1 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | 1 | 2i | -2i | 0 | 0 | 1 | -1 | -√-3 | √-3 | -√3 | √3 | i | -i | -i | i | complex lifted from C4○D12 |
| ρ21 | 2 | -2 | -2 | 2 | 0 | -1 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | 1 | -2i | 2i | 0 | 0 | 1 | -1 | -√-3 | √-3 | √3 | -√3 | -i | i | i | -i | complex lifted from C4○D12 |
| ρ22 | 2 | -2 | -2 | 2 | 0 | -1 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | 1 | 2i | -2i | 0 | 0 | 1 | -1 | √-3 | -√-3 | √3 | -√3 | i | -i | -i | i | complex lifted from C4○D12 |
| ρ23 | 4 | -4 | -4 | 4 | 0 | -2 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from S3×D4 |
| ρ24 | 4 | 4 | 4 | 4 | 0 | -2 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from S3×D4 |
| ρ25 | 4 | -4 | 4 | -4 | 0 | 4 | 0 | 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 | 4 | 0 | 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 | -2 | 0 | 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 | -2 | 0 | 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 | -2 | 0 | 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 Q16⋊S3 |
| ρ30 | 4 | -4 | 4 | -4 | 0 | -2 | 0 | 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 Q16⋊S3 |
►On 96 points
Generators in S96
(1 17 76)(2 77 18)(3 19 78)(4 79 20)(5 21 80)(6 73 22)(7 23 74)(8 75 24)(9 55 65)(10 66 56)(11 49 67)(12 68 50)(13 51 69)(14 70 52)(15 53 71)(16 72 54)(25 89 48)(26 41 90)(27 91 42)(28 43 92)(29 93 44)(30 45 94)(31 95 46)(32 47 96)(33 61 84)(34 85 62)(35 63 86)(36 87 64)(37 57 88)(38 81 58)(39 59 82)(40 83 60)
(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 12 61 26)(2 15 62 29)(3 10 63 32)(4 13 64 27)(5 16 57 30)(6 11 58 25)(7 14 59 28)(8 9 60 31)(17 68 84 41)(18 71 85 44)(19 66 86 47)(20 69 87 42)(21 72 88 45)(22 67 81 48)(23 70 82 43)(24 65 83 46)(33 90 76 50)(34 93 77 53)(35 96 78 56)(36 91 79 51)(37 94 80 54)(38 89 73 49)(39 92 74 52)(40 95 75 55)
(1 57)(2 62)(3 59)(4 64)(5 61)(6 58)(7 63)(8 60)(9 13)(11 15)(17 37)(18 34)(19 39)(20 36)(21 33)(22 38)(23 35)(24 40)(25 29)(27 31)(41 90)(42 95)(43 92)(44 89)(45 94)(46 91)(47 96)(48 93)(49 71)(50 68)(51 65)(52 70)(53 67)(54 72)(55 69)(56 66)(73 81)(74 86)(75 83)(76 88)(77 85)(78 82)(79 87)(80 84)
G:=sub<Sym(96)| (1,17,76)(2,77,18)(3,19,78)(4,79,20)(5,21,80)(6,73,22)(7,23,74)(8,75,24)(9,55,65)(10,66,56)(11,49,67)(12,68,50)(13,51,69)(14,70,52)(15,53,71)(16,72,54)(25,89,48)(26,41,90)(27,91,42)(28,43,92)(29,93,44)(30,45,94)(31,95,46)(32,47,96)(33,61,84)(34,85,62)(35,63,86)(36,87,64)(37,57,88)(38,81,58)(39,59,82)(40,83,60), (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), (1,12,61,26)(2,15,62,29)(3,10,63,32)(4,13,64,27)(5,16,57,30)(6,11,58,25)(7,14,59,28)(8,9,60,31)(17,68,84,41)(18,71,85,44)(19,66,86,47)(20,69,87,42)(21,72,88,45)(22,67,81,48)(23,70,82,43)(24,65,83,46)(33,90,76,50)(34,93,77,53)(35,96,78,56)(36,91,79,51)(37,94,80,54)(38,89,73,49)(39,92,74,52)(40,95,75,55), (1,57)(2,62)(3,59)(4,64)(5,61)(6,58)(7,63)(8,60)(9,13)(11,15)(17,37)(18,34)(19,39)(20,36)(21,33)(22,38)(23,35)(24,40)(25,29)(27,31)(41,90)(42,95)(43,92)(44,89)(45,94)(46,91)(47,96)(48,93)(49,71)(50,68)(51,65)(52,70)(53,67)(54,72)(55,69)(56,66)(73,81)(74,86)(75,83)(76,88)(77,85)(78,82)(79,87)(80,84)>;
G:=Group( (1,17,76)(2,77,18)(3,19,78)(4,79,20)(5,21,80)(6,73,22)(7,23,74)(8,75,24)(9,55,65)(10,66,56)(11,49,67)(12,68,50)(13,51,69)(14,70,52)(15,53,71)(16,72,54)(25,89,48)(26,41,90)(27,91,42)(28,43,92)(29,93,44)(30,45,94)(31,95,46)(32,47,96)(33,61,84)(34,85,62)(35,63,86)(36,87,64)(37,57,88)(38,81,58)(39,59,82)(40,83,60), (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), (1,12,61,26)(2,15,62,29)(3,10,63,32)(4,13,64,27)(5,16,57,30)(6,11,58,25)(7,14,59,28)(8,9,60,31)(17,68,84,41)(18,71,85,44)(19,66,86,47)(20,69,87,42)(21,72,88,45)(22,67,81,48)(23,70,82,43)(24,65,83,46)(33,90,76,50)(34,93,77,53)(35,96,78,56)(36,91,79,51)(37,94,80,54)(38,89,73,49)(39,92,74,52)(40,95,75,55), (1,57)(2,62)(3,59)(4,64)(5,61)(6,58)(7,63)(8,60)(9,13)(11,15)(17,37)(18,34)(19,39)(20,36)(21,33)(22,38)(23,35)(24,40)(25,29)(27,31)(41,90)(42,95)(43,92)(44,89)(45,94)(46,91)(47,96)(48,93)(49,71)(50,68)(51,65)(52,70)(53,67)(54,72)(55,69)(56,66)(73,81)(74,86)(75,83)(76,88)(77,85)(78,82)(79,87)(80,84) );
G=PermutationGroup([[(1,17,76),(2,77,18),(3,19,78),(4,79,20),(5,21,80),(6,73,22),(7,23,74),(8,75,24),(9,55,65),(10,66,56),(11,49,67),(12,68,50),(13,51,69),(14,70,52),(15,53,71),(16,72,54),(25,89,48),(26,41,90),(27,91,42),(28,43,92),(29,93,44),(30,45,94),(31,95,46),(32,47,96),(33,61,84),(34,85,62),(35,63,86),(36,87,64),(37,57,88),(38,81,58),(39,59,82),(40,83,60)], [(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)], [(1,12,61,26),(2,15,62,29),(3,10,63,32),(4,13,64,27),(5,16,57,30),(6,11,58,25),(7,14,59,28),(8,9,60,31),(17,68,84,41),(18,71,85,44),(19,66,86,47),(20,69,87,42),(21,72,88,45),(22,67,81,48),(23,70,82,43),(24,65,83,46),(33,90,76,50),(34,93,77,53),(35,96,78,56),(36,91,79,51),(37,94,80,54),(38,89,73,49),(39,92,74,52),(40,95,75,55)], [(1,57),(2,62),(3,59),(4,64),(5,61),(6,58),(7,63),(8,60),(9,13),(11,15),(17,37),(18,34),(19,39),(20,36),(21,33),(22,38),(23,35),(24,40),(25,29),(27,31),(41,90),(42,95),(43,92),(44,89),(45,94),(46,91),(47,96),(48,93),(49,71),(50,68),(51,65),(52,70),(53,67),(54,72),(55,69),(56,66),(73,81),(74,86),(75,83),(76,88),(77,85),(78,82),(79,87),(80,84)]])
Matrix representation of C3⋊C8.D4 ►in GL6(𝔽73)
| 0 | 72 | 0 | 0 | 0 | 0 |
| 1 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 72 | 72 | 1 | 0 |
| 0 | 0 | 1 | 0 | 0 | 72 |
| 0 | 0 | 0 | 0 | 0 | 72 |
| 0 | 0 | 0 | 0 | 1 | 72 |
| 0 | 27 | 0 | 0 | 0 | 0 |
| 27 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 53 | 53 | 62 | 20 |
| 0 | 0 | 0 | 0 | 62 | 0 |
| 0 | 0 | 0 | 53 | 62 | 62 |
| 0 | 0 | 53 | 53 | 51 | 31 |
| 7 | 59 | 0 | 0 | 0 | 0 |
| 14 | 66 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 66 | 33 | 40 |
| 0 | 0 | 0 | 53 | 33 | 33 |
| 0 | 0 | 66 | 59 | 20 | 7 |
| 0 | 0 | 7 | 66 | 0 | 13 |
| 0 | 72 | 0 | 0 | 0 | 0 |
| 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 72 |
| 0 | 0 | 1 | 0 | 0 | 72 |
| 0 | 0 | 0 | 0 | 1 | 72 |
| 0 | 0 | 0 | 0 | 0 | 72 |
G:=sub<GL(6,GF(73))| [0,1,0,0,0,0,72,72,0,0,0,0,0,0,72,1,0,0,0,0,72,0,0,0,0,0,1,0,0,1,0,0,0,72,72,72],[0,27,0,0,0,0,27,0,0,0,0,0,0,0,53,0,0,53,0,0,53,0,53,53,0,0,62,62,62,51,0,0,20,0,62,31],[7,14,0,0,0,0,59,66,0,0,0,0,0,0,60,0,66,7,0,0,66,53,59,66,0,0,33,33,20,0,0,0,40,33,7,13],[0,72,0,0,0,0,72,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,72,72,72,72] >;
C3⋊C8.D4 in GAP, Magma, Sage, TeX
C_3\rtimes C_8.D_4
% in TeX
G:=Group("C3:C8.D4"); // GroupNames label
G:=SmallGroup(192,375);
// by ID
G=gap.SmallGroup(192,375);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,253,344,1094,135,184,570,297,136,6278]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^8=c^4=d^2=1,b*a*b^-1=d*a*d=a^-1,a*c=c*a,c*b*c^-1=b^3,d*b*d=b^5,d*c*d=b^4*c^-1>;
// generators/relations
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