metabelian, supersoluble, monomial, A-group
Aliases: C33⋊5C4, C32⋊5Dic3, C3⋊(C3⋊Dic3), C6.3(C3⋊S3), (C3×C6).10S3, C2.(C33⋊C2), (C32×C6).3C2, SmallGroup(108,34)
Series: Derived ►Chief ►Lower central ►Upper central
| C33 — C33⋊5C4 |
Generators and relations for C33⋊5C4
G = < a,b,c,d | a3=b3=c3=d4=1, ab=ba, ac=ca, dad-1=a-1, bc=cb, dbd-1=b-1, dcd-1=c-1 >
Subgroups: 240 in 84 conjugacy classes, 57 normal (5 characteristic)
C1, C2, C3, C4, C6, C32, Dic3, C3×C6, C33, C3⋊Dic3, C32×C6, C33⋊5C4
Quotients: C1, C2, C4, S3, Dic3, C3⋊S3, C3⋊Dic3, C33⋊C2, C33⋊5C4
Character table of C33⋊5C4
| class | 1 | 2 | 3A | 3B | 3C | 3D | 3E | 3F | 3G | 3H | 3I | 3J | 3K | 3L | 3M | 4A | 4B | 6A | 6B | 6C | 6D | 6E | 6F | 6G | 6H | 6I | 6J | 6K | 6L | 6M | |
| size | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 27 | 27 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |
| 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 | -i | i | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 4 |
| ρ4 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | i | -i | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 4 |
| ρ5 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | 2 | -1 | orthogonal lifted from S3 |
| ρ6 | 2 | 2 | -1 | -1 | 2 | -1 | 2 | -1 | 2 | -1 | -1 | -1 | -1 | 2 | -1 | 0 | 0 | -1 | 2 | -1 | 2 | -1 | 2 | -1 | -1 | -1 | -1 | 2 | -1 | -1 | orthogonal lifted from S3 |
| ρ7 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | 0 | 0 | -1 | -1 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | 2 | orthogonal lifted from S3 |
| ρ8 | 2 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | 2 | -1 | 2 | -1 | -1 | -1 | 0 | 0 | -1 | 2 | -1 | -1 | 2 | -1 | 2 | -1 | 2 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ9 | 2 | 2 | -1 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | -1 | 2 | -1 | -1 | 0 | 0 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | -1 | 2 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ10 | 2 | 2 | -1 | 2 | -1 | 2 | -1 | -1 | -1 | 2 | -1 | -1 | -1 | 2 | -1 | 0 | 0 | 2 | -1 | 2 | -1 | -1 | -1 | 2 | -1 | -1 | -1 | 2 | -1 | -1 | orthogonal lifted from S3 |
| ρ11 | 2 | 2 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | -1 | 0 | 0 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | -1 | 2 | orthogonal lifted from S3 |
| ρ12 | 2 | 2 | -1 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | 2 | -1 | 2 | -1 | -1 | 0 | 0 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | 2 | -1 | 2 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ13 | 2 | 2 | 2 | -1 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 0 | 0 | -1 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | orthogonal lifted from S3 |
| ρ14 | 2 | 2 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | -1 | 0 | 0 | 2 | -1 | -1 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ15 | 2 | 2 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 0 | 0 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | orthogonal lifted from S3 |
| ρ16 | 2 | 2 | -1 | -1 | -1 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 0 | 0 | -1 | -1 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | -1 | orthogonal lifted from S3 |
| ρ17 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | -1 | -1 | -1 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | -1 | -1 | -1 | 2 | -1 | orthogonal lifted from S3 |
| ρ18 | 2 | -2 | -1 | -1 | 2 | -1 | 2 | -1 | 2 | -1 | -1 | -1 | -1 | 2 | -1 | 0 | 0 | 1 | -2 | 1 | -2 | 1 | -2 | 1 | 1 | 1 | 1 | -2 | 1 | 1 | symplectic lifted from Dic3, Schur index 2 |
| ρ19 | 2 | -2 | -1 | -1 | -1 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 0 | 0 | 1 | 1 | -2 | -2 | -2 | 1 | 1 | 1 | 1 | 1 | 1 | -2 | 1 | symplectic lifted from Dic3, Schur index 2 |
| ρ20 | 2 | -2 | -1 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | -1 | 2 | -1 | -1 | 0 | 0 | -2 | 1 | 1 | 1 | -2 | -2 | 1 | 1 | 1 | -2 | 1 | 1 | 1 | symplectic lifted from Dic3, Schur index 2 |
| ρ21 | 2 | -2 | 2 | -1 | -1 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | 0 | 0 | 1 | 1 | 1 | 1 | -2 | 1 | 1 | -2 | 1 | 1 | -2 | 1 | -2 | symplectic lifted from Dic3, Schur index 2 |
| ρ22 | 2 | -2 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | 2 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -2 | -2 | -2 | -2 | 1 | symplectic lifted from Dic3, Schur index 2 |
| ρ23 | 2 | -2 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | -1 | 0 | 0 | -2 | 1 | 1 | -2 | 1 | 1 | 1 | -2 | -2 | 1 | 1 | 1 | 1 | symplectic lifted from Dic3, Schur index 2 |
| ρ24 | 2 | -2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | 2 | -1 | 2 | -1 | -1 | -1 | 0 | 0 | 1 | -2 | 1 | 1 | -2 | 1 | -2 | 1 | -2 | 1 | 1 | 1 | 1 | symplectic lifted from Dic3, Schur index 2 |
| ρ25 | 2 | -2 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | -1 | 0 | 0 | 1 | 1 | -2 | 1 | 1 | -2 | 1 | 1 | -2 | 1 | 1 | 1 | -2 | symplectic lifted from Dic3, Schur index 2 |
| ρ26 | 2 | -2 | -1 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | 2 | -1 | 2 | -1 | -1 | 0 | 0 | 1 | -2 | -2 | 1 | 1 | 1 | 1 | -2 | 1 | -2 | 1 | 1 | 1 | symplectic lifted from Dic3, Schur index 2 |
| ρ27 | 2 | -2 | 2 | -1 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 0 | 0 | 1 | 1 | 1 | -2 | 1 | 1 | -2 | 1 | 1 | -2 | 1 | 1 | -2 | symplectic lifted from Dic3, Schur index 2 |
| ρ28 | 2 | -2 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | -1 | -1 | -1 | 2 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | -2 | -2 | -2 | 1 | 1 | 1 | -2 | 1 | symplectic lifted from Dic3, Schur index 2 |
| ρ29 | 2 | -2 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 0 | 0 | -2 | -2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -2 | -2 | symplectic lifted from Dic3, Schur index 2 |
| ρ30 | 2 | -2 | -1 | 2 | -1 | 2 | -1 | -1 | -1 | 2 | -1 | -1 | -1 | 2 | -1 | 0 | 0 | -2 | 1 | -2 | 1 | 1 | 1 | -2 | 1 | 1 | 1 | -2 | 1 | 1 | symplectic lifted from Dic3, Schur index 2 |
►Regular action on 108 points
Generators in S108
(1 27 74)(2 75 28)(3 25 76)(4 73 26)(5 101 41)(6 42 102)(7 103 43)(8 44 104)(9 81 47)(10 48 82)(11 83 45)(12 46 84)(13 61 49)(14 50 62)(15 63 51)(16 52 64)(17 55 68)(18 65 56)(19 53 66)(20 67 54)(21 35 70)(22 71 36)(23 33 72)(24 69 34)(29 99 38)(30 39 100)(31 97 40)(32 37 98)(57 78 90)(58 91 79)(59 80 92)(60 89 77)(85 105 95)(86 96 106)(87 107 93)(88 94 108)
(1 49 31)(2 32 50)(3 51 29)(4 30 52)(5 80 56)(6 53 77)(7 78 54)(8 55 79)(9 93 22)(10 23 94)(11 95 24)(12 21 96)(13 97 27)(14 28 98)(15 99 25)(16 26 100)(17 91 104)(18 101 92)(19 89 102)(20 103 90)(33 108 48)(34 45 105)(35 106 46)(36 47 107)(37 62 75)(38 76 63)(39 64 73)(40 74 61)(41 59 65)(42 66 60)(43 57 67)(44 68 58)(69 83 85)(70 86 84)(71 81 87)(72 88 82)
(1 22 43)(2 44 23)(3 24 41)(4 42 21)(5 25 69)(6 70 26)(7 27 71)(8 72 28)(9 57 49)(10 50 58)(11 59 51)(12 52 60)(13 81 78)(14 79 82)(15 83 80)(16 77 84)(17 108 37)(18 38 105)(19 106 39)(20 40 107)(29 95 65)(30 66 96)(31 93 67)(32 68 94)(33 75 104)(34 101 76)(35 73 102)(36 103 74)(45 92 63)(46 64 89)(47 90 61)(48 62 91)(53 86 100)(54 97 87)(55 88 98)(56 99 85)
(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)(97 98 99 100)(101 102 103 104)(105 106 107 108)
G:=sub<Sym(108)| (1,27,74)(2,75,28)(3,25,76)(4,73,26)(5,101,41)(6,42,102)(7,103,43)(8,44,104)(9,81,47)(10,48,82)(11,83,45)(12,46,84)(13,61,49)(14,50,62)(15,63,51)(16,52,64)(17,55,68)(18,65,56)(19,53,66)(20,67,54)(21,35,70)(22,71,36)(23,33,72)(24,69,34)(29,99,38)(30,39,100)(31,97,40)(32,37,98)(57,78,90)(58,91,79)(59,80,92)(60,89,77)(85,105,95)(86,96,106)(87,107,93)(88,94,108), (1,49,31)(2,32,50)(3,51,29)(4,30,52)(5,80,56)(6,53,77)(7,78,54)(8,55,79)(9,93,22)(10,23,94)(11,95,24)(12,21,96)(13,97,27)(14,28,98)(15,99,25)(16,26,100)(17,91,104)(18,101,92)(19,89,102)(20,103,90)(33,108,48)(34,45,105)(35,106,46)(36,47,107)(37,62,75)(38,76,63)(39,64,73)(40,74,61)(41,59,65)(42,66,60)(43,57,67)(44,68,58)(69,83,85)(70,86,84)(71,81,87)(72,88,82), (1,22,43)(2,44,23)(3,24,41)(4,42,21)(5,25,69)(6,70,26)(7,27,71)(8,72,28)(9,57,49)(10,50,58)(11,59,51)(12,52,60)(13,81,78)(14,79,82)(15,83,80)(16,77,84)(17,108,37)(18,38,105)(19,106,39)(20,40,107)(29,95,65)(30,66,96)(31,93,67)(32,68,94)(33,75,104)(34,101,76)(35,73,102)(36,103,74)(45,92,63)(46,64,89)(47,90,61)(48,62,91)(53,86,100)(54,97,87)(55,88,98)(56,99,85), (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)(97,98,99,100)(101,102,103,104)(105,106,107,108)>;
G:=Group( (1,27,74)(2,75,28)(3,25,76)(4,73,26)(5,101,41)(6,42,102)(7,103,43)(8,44,104)(9,81,47)(10,48,82)(11,83,45)(12,46,84)(13,61,49)(14,50,62)(15,63,51)(16,52,64)(17,55,68)(18,65,56)(19,53,66)(20,67,54)(21,35,70)(22,71,36)(23,33,72)(24,69,34)(29,99,38)(30,39,100)(31,97,40)(32,37,98)(57,78,90)(58,91,79)(59,80,92)(60,89,77)(85,105,95)(86,96,106)(87,107,93)(88,94,108), (1,49,31)(2,32,50)(3,51,29)(4,30,52)(5,80,56)(6,53,77)(7,78,54)(8,55,79)(9,93,22)(10,23,94)(11,95,24)(12,21,96)(13,97,27)(14,28,98)(15,99,25)(16,26,100)(17,91,104)(18,101,92)(19,89,102)(20,103,90)(33,108,48)(34,45,105)(35,106,46)(36,47,107)(37,62,75)(38,76,63)(39,64,73)(40,74,61)(41,59,65)(42,66,60)(43,57,67)(44,68,58)(69,83,85)(70,86,84)(71,81,87)(72,88,82), (1,22,43)(2,44,23)(3,24,41)(4,42,21)(5,25,69)(6,70,26)(7,27,71)(8,72,28)(9,57,49)(10,50,58)(11,59,51)(12,52,60)(13,81,78)(14,79,82)(15,83,80)(16,77,84)(17,108,37)(18,38,105)(19,106,39)(20,40,107)(29,95,65)(30,66,96)(31,93,67)(32,68,94)(33,75,104)(34,101,76)(35,73,102)(36,103,74)(45,92,63)(46,64,89)(47,90,61)(48,62,91)(53,86,100)(54,97,87)(55,88,98)(56,99,85), (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)(97,98,99,100)(101,102,103,104)(105,106,107,108) );
G=PermutationGroup([[(1,27,74),(2,75,28),(3,25,76),(4,73,26),(5,101,41),(6,42,102),(7,103,43),(8,44,104),(9,81,47),(10,48,82),(11,83,45),(12,46,84),(13,61,49),(14,50,62),(15,63,51),(16,52,64),(17,55,68),(18,65,56),(19,53,66),(20,67,54),(21,35,70),(22,71,36),(23,33,72),(24,69,34),(29,99,38),(30,39,100),(31,97,40),(32,37,98),(57,78,90),(58,91,79),(59,80,92),(60,89,77),(85,105,95),(86,96,106),(87,107,93),(88,94,108)], [(1,49,31),(2,32,50),(3,51,29),(4,30,52),(5,80,56),(6,53,77),(7,78,54),(8,55,79),(9,93,22),(10,23,94),(11,95,24),(12,21,96),(13,97,27),(14,28,98),(15,99,25),(16,26,100),(17,91,104),(18,101,92),(19,89,102),(20,103,90),(33,108,48),(34,45,105),(35,106,46),(36,47,107),(37,62,75),(38,76,63),(39,64,73),(40,74,61),(41,59,65),(42,66,60),(43,57,67),(44,68,58),(69,83,85),(70,86,84),(71,81,87),(72,88,82)], [(1,22,43),(2,44,23),(3,24,41),(4,42,21),(5,25,69),(6,70,26),(7,27,71),(8,72,28),(9,57,49),(10,50,58),(11,59,51),(12,52,60),(13,81,78),(14,79,82),(15,83,80),(16,77,84),(17,108,37),(18,38,105),(19,106,39),(20,40,107),(29,95,65),(30,66,96),(31,93,67),(32,68,94),(33,75,104),(34,101,76),(35,73,102),(36,103,74),(45,92,63),(46,64,89),(47,90,61),(48,62,91),(53,86,100),(54,97,87),(55,88,98),(56,99,85)], [(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),(97,98,99,100),(101,102,103,104),(105,106,107,108)]])
C33⋊5C4 is a maximal subgroup of
S3×C3⋊Dic3 Dic3×C3⋊S3 C33⋊6D4 C33⋊4Q8 C33⋊8Q8 C4×C33⋊C2 C33⋊15D4 C33⋊C12 C33⋊4C12 C32⋊5Dic9 C34⋊8C4 C32⋊4CSU2(𝔽3) C62⋊10Dic3
C33⋊5C4 is a maximal quotient of
C33⋊7C8 C32⋊5Dic9 He3⋊6Dic3 C34⋊8C4 C62⋊10Dic3
Matrix representation of C33⋊5C4 ►in GL7(𝔽13)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 12 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 | 12 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 12 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 9 | 0 | 0 | 0 |
| 0 | 0 | 0 | 7 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 12 | 12 |
| 5 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 3 | 6 | 0 | 0 | 0 | 0 |
| 0 | 3 | 10 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 5 | 5 | 0 | 0 |
| 0 | 0 | 0 | 3 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 10 | 7 |
| 0 | 0 | 0 | 0 | 0 | 10 | 3 |
G:=sub<GL(7,GF(13))| [1,0,0,0,0,0,0,0,0,12,0,0,0,0,0,1,12,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,12,1,0,0,0,0,0,12,0],[1,0,0,0,0,0,0,0,0,12,0,0,0,0,0,1,12,0,0,0,0,0,0,0,9,7,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,12,0,0,0,0,0,1,12],[5,0,0,0,0,0,0,0,3,3,0,0,0,0,0,6,10,0,0,0,0,0,0,0,5,3,0,0,0,0,0,5,8,0,0,0,0,0,0,0,10,10,0,0,0,0,0,7,3] >;
C33⋊5C4 in GAP, Magma, Sage, TeX
C_3^3\rtimes_5C_4
% in TeX
G:=Group("C3^3:5C4"); // GroupNames label
G:=SmallGroup(108,34);
// by ID
G=gap.SmallGroup(108,34);
# by ID
G:=PCGroup([5,-2,-2,-3,-3,-3,10,122,483,1804]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^3=c^3=d^4=1,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=c^-1>;
// generators/relations
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