direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C3×C22.33C24, C6.1552+ 1+4, C6.1132- 1+4, (C4×D4)⋊11C6, C22⋊Q8⋊8C6, (D4×C12)⋊40C2, C4⋊D4.8C6, C42.C2⋊4C6, C42⋊2C2⋊4C6, C42.37(C2×C6), (C2×C6).359C24, C22.D4⋊5C6, (C2×C12).668C23, (C4×C12).278C22, (C6×D4).217C22, (C22×C6).94C23, C23.42(C22×C6), C22.33(C23×C6), (C6×Q8).181C22, C2.5(C3×2- 1+4), C2.7(C3×2+ 1+4), (C22×C12).38C22, (C6×C4⋊C4)⋊46C2, (C2×C4⋊C4)⋊19C6, C4⋊C4.68(C2×C6), C2.16(C6×C4○D4), (C2×D4).31(C2×C6), C6.235(C2×C4○D4), (C3×C22⋊Q8)⋊35C2, (C2×Q8).26(C2×C6), C22.5(C3×C4○D4), (C2×C6).53(C4○D4), (C3×C4⋊D4).18C2, C22⋊C4.15(C2×C6), (C2×C4).26(C22×C6), (C22×C4).64(C2×C6), (C3×C42.C2)⋊21C2, (C3×C42⋊2C2)⋊13C2, (C3×C4⋊C4).392C22, (C3×C22.D4)⋊24C2, (C3×C22⋊C4).85C22, SmallGroup(192,1428)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×C22.33C24
G = < a,b,c,d,e,f,g | a3=b2=c2=d2=g2=1, e2=c, f2=b, ab=ba, ac=ca, ad=da, ae=ea, af=fa, ag=ga, bc=cb, ede-1=gdg=bd=db, fef-1=be=eb, bf=fb, bg=gb, fdf-1=cd=dc, ce=ec, cf=fc, cg=gc, eg=ge, fg=gf >
Subgroups: 322 in 218 conjugacy classes, 146 normal (38 characteristic)
C1, C2, C2, C3, C4, C22, C22, C22, C6, C6, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, C12, C2×C6, C2×C6, C2×C6, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×C12, C2×C12, C2×C12, C3×D4, C3×Q8, C22×C6, C22×C6, C2×C4⋊C4, C4×D4, C4⋊D4, C22⋊Q8, C22⋊Q8, C22.D4, C42.C2, C42⋊2C2, C4×C12, C3×C22⋊C4, C3×C4⋊C4, C3×C4⋊C4, C22×C12, C22×C12, C6×D4, C6×D4, C6×Q8, C22.33C24, C6×C4⋊C4, D4×C12, C3×C4⋊D4, C3×C22⋊Q8, C3×C22⋊Q8, C3×C22.D4, C3×C42.C2, C3×C42⋊2C2, C3×C22.33C24
Quotients: C1, C2, C3, C22, C6, C23, C2×C6, C4○D4, C24, C22×C6, C2×C4○D4, 2+ 1+4, 2- 1+4, C3×C4○D4, C23×C6, C22.33C24, C6×C4○D4, C3×2+ 1+4, C3×2- 1+4, C3×C22.33C24
►On 96 points
Generators in S96
(1 57 9)(2 58 10)(3 59 11)(4 60 12)(5 28 54)(6 25 55)(7 26 56)(8 27 53)(13 17 61)(14 18 62)(15 19 63)(16 20 64)(21 65 69)(22 66 70)(23 67 71)(24 68 72)(29 73 77)(30 74 78)(31 75 79)(32 76 80)(33 37 81)(34 38 82)(35 39 83)(36 40 84)(41 85 89)(42 86 90)(43 87 91)(44 88 92)(45 51 93)(46 52 94)(47 49 95)(48 50 96)
(1 75)(2 76)(3 73)(4 74)(5 94)(6 95)(7 96)(8 93)(9 31)(10 32)(11 29)(12 30)(13 35)(14 36)(15 33)(16 34)(17 39)(18 40)(19 37)(20 38)(21 43)(22 44)(23 41)(24 42)(25 47)(26 48)(27 45)(28 46)(49 55)(50 56)(51 53)(52 54)(57 79)(58 80)(59 77)(60 78)(61 83)(62 84)(63 81)(64 82)(65 87)(66 88)(67 85)(68 86)(69 91)(70 92)(71 89)(72 90)
(1 3)(2 4)(5 7)(6 8)(9 11)(10 12)(13 15)(14 16)(17 19)(18 20)(21 23)(22 24)(25 27)(26 28)(29 31)(30 32)(33 35)(34 36)(37 39)(38 40)(41 43)(42 44)(45 47)(46 48)(49 51)(50 52)(53 55)(54 56)(57 59)(58 60)(61 63)(62 64)(65 67)(66 68)(69 71)(70 72)(73 75)(74 76)(77 79)(78 80)(81 83)(82 84)(85 87)(86 88)(89 91)(90 92)(93 95)(94 96)
(2 76)(4 74)(5 7)(6 93)(8 95)(10 32)(12 30)(13 35)(15 33)(17 39)(19 37)(21 23)(22 42)(24 44)(25 45)(26 28)(27 47)(41 43)(46 48)(49 53)(50 52)(51 55)(54 56)(58 80)(60 78)(61 83)(63 81)(65 67)(66 86)(68 88)(69 71)(70 90)(72 92)(85 87)(89 91)(94 96)
(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 87 75 65)(2 66 76 88)(3 85 73 67)(4 68 74 86)(5 82 94 64)(6 61 95 83)(7 84 96 62)(8 63 93 81)(9 43 31 21)(10 22 32 44)(11 41 29 23)(12 24 30 42)(13 47 35 25)(14 26 36 48)(15 45 33 27)(16 28 34 46)(17 49 39 55)(18 56 40 50)(19 51 37 53)(20 54 38 52)(57 91 79 69)(58 70 80 92)(59 89 77 71)(60 72 78 90)
(1 13)(2 14)(3 15)(4 16)(5 24)(6 21)(7 22)(8 23)(9 61)(10 62)(11 63)(12 64)(17 57)(18 58)(19 59)(20 60)(25 65)(26 66)(27 67)(28 68)(29 81)(30 82)(31 83)(32 84)(33 73)(34 74)(35 75)(36 76)(37 77)(38 78)(39 79)(40 80)(41 93)(42 94)(43 95)(44 96)(45 85)(46 86)(47 87)(48 88)(49 91)(50 92)(51 89)(52 90)(53 71)(54 72)(55 69)(56 70)
G:=sub<Sym(96)| (1,57,9)(2,58,10)(3,59,11)(4,60,12)(5,28,54)(6,25,55)(7,26,56)(8,27,53)(13,17,61)(14,18,62)(15,19,63)(16,20,64)(21,65,69)(22,66,70)(23,67,71)(24,68,72)(29,73,77)(30,74,78)(31,75,79)(32,76,80)(33,37,81)(34,38,82)(35,39,83)(36,40,84)(41,85,89)(42,86,90)(43,87,91)(44,88,92)(45,51,93)(46,52,94)(47,49,95)(48,50,96), (1,75)(2,76)(3,73)(4,74)(5,94)(6,95)(7,96)(8,93)(9,31)(10,32)(11,29)(12,30)(13,35)(14,36)(15,33)(16,34)(17,39)(18,40)(19,37)(20,38)(21,43)(22,44)(23,41)(24,42)(25,47)(26,48)(27,45)(28,46)(49,55)(50,56)(51,53)(52,54)(57,79)(58,80)(59,77)(60,78)(61,83)(62,84)(63,81)(64,82)(65,87)(66,88)(67,85)(68,86)(69,91)(70,92)(71,89)(72,90), (1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36)(37,39)(38,40)(41,43)(42,44)(45,47)(46,48)(49,51)(50,52)(53,55)(54,56)(57,59)(58,60)(61,63)(62,64)(65,67)(66,68)(69,71)(70,72)(73,75)(74,76)(77,79)(78,80)(81,83)(82,84)(85,87)(86,88)(89,91)(90,92)(93,95)(94,96), (2,76)(4,74)(5,7)(6,93)(8,95)(10,32)(12,30)(13,35)(15,33)(17,39)(19,37)(21,23)(22,42)(24,44)(25,45)(26,28)(27,47)(41,43)(46,48)(49,53)(50,52)(51,55)(54,56)(58,80)(60,78)(61,83)(63,81)(65,67)(66,86)(68,88)(69,71)(70,90)(72,92)(85,87)(89,91)(94,96), (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), (1,87,75,65)(2,66,76,88)(3,85,73,67)(4,68,74,86)(5,82,94,64)(6,61,95,83)(7,84,96,62)(8,63,93,81)(9,43,31,21)(10,22,32,44)(11,41,29,23)(12,24,30,42)(13,47,35,25)(14,26,36,48)(15,45,33,27)(16,28,34,46)(17,49,39,55)(18,56,40,50)(19,51,37,53)(20,54,38,52)(57,91,79,69)(58,70,80,92)(59,89,77,71)(60,72,78,90), (1,13)(2,14)(3,15)(4,16)(5,24)(6,21)(7,22)(8,23)(9,61)(10,62)(11,63)(12,64)(17,57)(18,58)(19,59)(20,60)(25,65)(26,66)(27,67)(28,68)(29,81)(30,82)(31,83)(32,84)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(41,93)(42,94)(43,95)(44,96)(45,85)(46,86)(47,87)(48,88)(49,91)(50,92)(51,89)(52,90)(53,71)(54,72)(55,69)(56,70)>;
G:=Group( (1,57,9)(2,58,10)(3,59,11)(4,60,12)(5,28,54)(6,25,55)(7,26,56)(8,27,53)(13,17,61)(14,18,62)(15,19,63)(16,20,64)(21,65,69)(22,66,70)(23,67,71)(24,68,72)(29,73,77)(30,74,78)(31,75,79)(32,76,80)(33,37,81)(34,38,82)(35,39,83)(36,40,84)(41,85,89)(42,86,90)(43,87,91)(44,88,92)(45,51,93)(46,52,94)(47,49,95)(48,50,96), (1,75)(2,76)(3,73)(4,74)(5,94)(6,95)(7,96)(8,93)(9,31)(10,32)(11,29)(12,30)(13,35)(14,36)(15,33)(16,34)(17,39)(18,40)(19,37)(20,38)(21,43)(22,44)(23,41)(24,42)(25,47)(26,48)(27,45)(28,46)(49,55)(50,56)(51,53)(52,54)(57,79)(58,80)(59,77)(60,78)(61,83)(62,84)(63,81)(64,82)(65,87)(66,88)(67,85)(68,86)(69,91)(70,92)(71,89)(72,90), (1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36)(37,39)(38,40)(41,43)(42,44)(45,47)(46,48)(49,51)(50,52)(53,55)(54,56)(57,59)(58,60)(61,63)(62,64)(65,67)(66,68)(69,71)(70,72)(73,75)(74,76)(77,79)(78,80)(81,83)(82,84)(85,87)(86,88)(89,91)(90,92)(93,95)(94,96), (2,76)(4,74)(5,7)(6,93)(8,95)(10,32)(12,30)(13,35)(15,33)(17,39)(19,37)(21,23)(22,42)(24,44)(25,45)(26,28)(27,47)(41,43)(46,48)(49,53)(50,52)(51,55)(54,56)(58,80)(60,78)(61,83)(63,81)(65,67)(66,86)(68,88)(69,71)(70,90)(72,92)(85,87)(89,91)(94,96), (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), (1,87,75,65)(2,66,76,88)(3,85,73,67)(4,68,74,86)(5,82,94,64)(6,61,95,83)(7,84,96,62)(8,63,93,81)(9,43,31,21)(10,22,32,44)(11,41,29,23)(12,24,30,42)(13,47,35,25)(14,26,36,48)(15,45,33,27)(16,28,34,46)(17,49,39,55)(18,56,40,50)(19,51,37,53)(20,54,38,52)(57,91,79,69)(58,70,80,92)(59,89,77,71)(60,72,78,90), (1,13)(2,14)(3,15)(4,16)(5,24)(6,21)(7,22)(8,23)(9,61)(10,62)(11,63)(12,64)(17,57)(18,58)(19,59)(20,60)(25,65)(26,66)(27,67)(28,68)(29,81)(30,82)(31,83)(32,84)(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80)(41,93)(42,94)(43,95)(44,96)(45,85)(46,86)(47,87)(48,88)(49,91)(50,92)(51,89)(52,90)(53,71)(54,72)(55,69)(56,70) );
G=PermutationGroup([[(1,57,9),(2,58,10),(3,59,11),(4,60,12),(5,28,54),(6,25,55),(7,26,56),(8,27,53),(13,17,61),(14,18,62),(15,19,63),(16,20,64),(21,65,69),(22,66,70),(23,67,71),(24,68,72),(29,73,77),(30,74,78),(31,75,79),(32,76,80),(33,37,81),(34,38,82),(35,39,83),(36,40,84),(41,85,89),(42,86,90),(43,87,91),(44,88,92),(45,51,93),(46,52,94),(47,49,95),(48,50,96)], [(1,75),(2,76),(3,73),(4,74),(5,94),(6,95),(7,96),(8,93),(9,31),(10,32),(11,29),(12,30),(13,35),(14,36),(15,33),(16,34),(17,39),(18,40),(19,37),(20,38),(21,43),(22,44),(23,41),(24,42),(25,47),(26,48),(27,45),(28,46),(49,55),(50,56),(51,53),(52,54),(57,79),(58,80),(59,77),(60,78),(61,83),(62,84),(63,81),(64,82),(65,87),(66,88),(67,85),(68,86),(69,91),(70,92),(71,89),(72,90)], [(1,3),(2,4),(5,7),(6,8),(9,11),(10,12),(13,15),(14,16),(17,19),(18,20),(21,23),(22,24),(25,27),(26,28),(29,31),(30,32),(33,35),(34,36),(37,39),(38,40),(41,43),(42,44),(45,47),(46,48),(49,51),(50,52),(53,55),(54,56),(57,59),(58,60),(61,63),(62,64),(65,67),(66,68),(69,71),(70,72),(73,75),(74,76),(77,79),(78,80),(81,83),(82,84),(85,87),(86,88),(89,91),(90,92),(93,95),(94,96)], [(2,76),(4,74),(5,7),(6,93),(8,95),(10,32),(12,30),(13,35),(15,33),(17,39),(19,37),(21,23),(22,42),(24,44),(25,45),(26,28),(27,47),(41,43),(46,48),(49,53),(50,52),(51,55),(54,56),(58,80),(60,78),(61,83),(63,81),(65,67),(66,86),(68,88),(69,71),(70,90),(72,92),(85,87),(89,91),(94,96)], [(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)], [(1,87,75,65),(2,66,76,88),(3,85,73,67),(4,68,74,86),(5,82,94,64),(6,61,95,83),(7,84,96,62),(8,63,93,81),(9,43,31,21),(10,22,32,44),(11,41,29,23),(12,24,30,42),(13,47,35,25),(14,26,36,48),(15,45,33,27),(16,28,34,46),(17,49,39,55),(18,56,40,50),(19,51,37,53),(20,54,38,52),(57,91,79,69),(58,70,80,92),(59,89,77,71),(60,72,78,90)], [(1,13),(2,14),(3,15),(4,16),(5,24),(6,21),(7,22),(8,23),(9,61),(10,62),(11,63),(12,64),(17,57),(18,58),(19,59),(20,60),(25,65),(26,66),(27,67),(28,68),(29,81),(30,82),(31,83),(32,84),(33,73),(34,74),(35,75),(36,76),(37,77),(38,78),(39,79),(40,80),(41,93),(42,94),(43,95),(44,96),(45,85),(46,86),(47,87),(48,88),(49,91),(50,92),(51,89),(52,90),(53,71),(54,72),(55,69),(56,70)]])
66 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3A | 3B | 4A | 4B | 4C | 4D | 4E | ··· | 4N | 6A | ··· | 6F | 6G | 6H | 6I | 6J | 6K | 6L | 6M | 6N | 12A | ··· | 12H | 12I | ··· | 12AB |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 6 | ··· | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 12 | ··· | 12 | 12 | ··· | 12 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
66 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | ||||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C3 | C6 | C6 | C6 | C6 | C6 | C6 | C6 | C4○D4 | C3×C4○D4 | 2+ 1+4 | 2- 1+4 | C3×2+ 1+4 | C3×2- 1+4 |
| kernel | C3×C22.33C24 | C6×C4⋊C4 | D4×C12 | C3×C4⋊D4 | C3×C22⋊Q8 | C3×C22.D4 | C3×C42.C2 | C3×C42⋊2C2 | C22.33C24 | C2×C4⋊C4 | C4×D4 | C4⋊D4 | C22⋊Q8 | C22.D4 | C42.C2 | C42⋊2C2 | C2×C6 | C22 | C6 | C6 | C2 | C2 |
| # reps | 1 | 1 | 2 | 1 | 3 | 4 | 2 | 2 | 2 | 2 | 4 | 2 | 6 | 8 | 4 | 4 | 4 | 8 | 1 | 1 | 2 | 2 |
Matrix representation of C3×C22.33C24 ►in GL6(𝔽13)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 0 | 0 | 0 |
| 0 | 0 | 0 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 0 |
| 0 | 0 | 0 | 0 | 0 | 9 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 5 | 0 | 0 | 0 | 0 | 0 |
| 0 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 11 | 0 | 6 |
| 0 | 0 | 11 | 0 | 6 | 0 |
| 0 | 0 | 0 | 6 | 0 | 2 |
| 0 | 0 | 6 | 0 | 2 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 1 | 0 | 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 |
G:=sub<GL(6,GF(13))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,9,0,0,0,0,0,0,9,0,0,0,0,0,0,9,0,0,0,0,0,0,9],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,12],[5,0,0,0,0,0,0,5,0,0,0,0,0,0,0,11,0,6,0,0,11,0,6,0,0,0,0,6,0,2,0,0,6,0,2,0],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,1,0,0,0,0,0,0,1,0,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0] >;
C3×C22.33C24 in GAP, Magma, Sage, TeX
C_3\times C_2^2._{33}C_2^4 % in TeX
G:=Group("C3xC2^2.33C2^4"); // GroupNames label
G:=SmallGroup(192,1428);
// by ID
G=gap.SmallGroup(192,1428);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-2,-2,701,680,2102,555,268,1571]);
// Polycyclic
G:=Group<a,b,c,d,e,f,g|a^3=b^2=c^2=d^2=g^2=1,e^2=c,f^2=b,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,a*g=g*a,b*c=c*b,e*d*e^-1=g*d*g=b*d=d*b,f*e*f^-1=b*e=e*b,b*f=f*b,b*g=g*b,f*d*f^-1=c*d=d*c,c*e=e*c,c*f=f*c,c*g=g*c,e*g=g*e,f*g=g*f>;
// generators/relations