direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C3×C23.38C23, C6.1112- 1+4, C4⋊Q8⋊9C6, C4.17(C6×D4), C22⋊Q8⋊5C6, C4.4D4⋊7C6, (C2×C12).348D4, C12.324(C2×D4), C42.36(C2×C6), (C22×Q8)⋊13C6, C22.22(C6×D4), C42⋊C2⋊11C6, (C2×C6).356C24, C22.D4⋊3C6, C6.191(C22×D4), (C4×C12).277C22, (C2×C12).665C23, (C6×D4).320C22, C23.10(C22×C6), C22.30(C23×C6), (C6×Q8).270C22, C2.3(C3×2- 1+4), (C22×C6).261C23, (C22×C12).446C22, (Q8×C2×C6)⋊17C2, C2.15(D4×C2×C6), (C3×C4⋊Q8)⋊30C2, C4⋊C4.27(C2×C6), (C2×C4).49(C3×D4), (C6×C4○D4).24C2, (C2×C4○D4).16C6, (C2×D4).65(C2×C6), (C2×C6).418(C2×D4), C22⋊C4.1(C2×C6), (C3×C22⋊Q8)⋊32C2, (C2×Q8).69(C2×C6), (C3×C4.4D4)⋊27C2, (C22×C4).62(C2×C6), (C2×C4).23(C22×C6), (C3×C42⋊C2)⋊32C2, (C3×C4⋊C4).247C22, (C3×C22.D4)⋊22C2, (C3×C22⋊C4).83C22, SmallGroup(192,1425)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×C23.38C23
G = < a,b,c,d,e,f,g | a3=b2=c2=d2=e2=1, f2=g2=c, ab=ba, ac=ca, ad=da, ae=ea, af=fa, ag=ga, ebe=bc=cb, bd=db, bf=fb, bg=gb, cd=dc, fef-1=ce=ec, gfg-1=cf=fc, cg=gc, geg-1=de=ed, df=fd, dg=gd >
Subgroups: 386 in 270 conjugacy classes, 162 normal (26 characteristic)
C1, C2, C2, C2, C3, C4, C4, C22, C22, C22, C6, C6, C6, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, C12, C12, C2×C6, C2×C6, C2×C6, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C2×Q8, C2×Q8, C4○D4, C2×C12, C2×C12, C2×C12, C3×D4, C3×Q8, C22×C6, C22×C6, C42⋊C2, C22⋊Q8, C22.D4, C4.4D4, C4⋊Q8, C22×Q8, C2×C4○D4, C4×C12, C3×C22⋊C4, C3×C4⋊C4, C22×C12, C22×C12, C6×D4, C6×D4, C6×Q8, C6×Q8, C6×Q8, C3×C4○D4, C23.38C23, C3×C42⋊C2, C3×C22⋊Q8, C3×C22.D4, C3×C4.4D4, C3×C4⋊Q8, Q8×C2×C6, C6×C4○D4, C3×C23.38C23
Quotients: C1, C2, C3, C22, C6, D4, C23, C2×C6, C2×D4, C24, C3×D4, C22×C6, C22×D4, 2- 1+4, C6×D4, C23×C6, C23.38C23, D4×C2×C6, C3×2- 1+4, C3×C23.38C23
►On 96 points
Generators in S96
(1 11 55)(2 12 56)(3 9 53)(4 10 54)(5 25 69)(6 26 70)(7 27 71)(8 28 72)(13 57 61)(14 58 62)(15 59 63)(16 60 64)(17 21 65)(18 22 66)(19 23 67)(20 24 68)(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 52 93)(46 49 94)(47 50 95)(48 51 96)
(1 59)(2 60)(3 57)(4 58)(5 21)(6 22)(7 23)(8 24)(9 61)(10 62)(11 63)(12 64)(13 53)(14 54)(15 55)(16 56)(17 69)(18 70)(19 71)(20 72)(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 90)(50 91)(51 92)(52 89)
(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)
(1 75)(2 76)(3 73)(4 74)(5 52)(6 49)(7 50)(8 51)(9 77)(10 78)(11 79)(12 80)(13 81)(14 82)(15 83)(16 84)(17 85)(18 86)(19 87)(20 88)(21 89)(22 90)(23 91)(24 92)(25 93)(26 94)(27 95)(28 96)(29 53)(30 54)(31 55)(32 56)(33 57)(34 58)(35 59)(36 60)(37 61)(38 62)(39 63)(40 64)(41 65)(42 66)(43 67)(44 68)(45 69)(46 70)(47 71)(48 72)
(1 4)(2 3)(5 51)(6 50)(7 49)(8 52)(9 12)(10 11)(13 14)(15 16)(17 86)(18 85)(19 88)(20 87)(21 90)(22 89)(23 92)(24 91)(25 96)(26 95)(27 94)(28 93)(29 32)(30 31)(33 34)(35 36)(37 38)(39 40)(41 66)(42 65)(43 68)(44 67)(45 72)(46 71)(47 70)(48 69)(53 56)(54 55)(57 58)(59 60)(61 62)(63 64)(73 76)(74 75)(77 80)(78 79)(81 82)(83 84)
(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 17 3 19)(2 20 4 18)(5 61 7 63)(6 64 8 62)(9 23 11 21)(10 22 12 24)(13 27 15 25)(14 26 16 28)(29 43 31 41)(30 42 32 44)(33 47 35 45)(34 46 36 48)(37 50 39 52)(38 49 40 51)(53 67 55 65)(54 66 56 68)(57 71 59 69)(58 70 60 72)(73 87 75 85)(74 86 76 88)(77 91 79 89)(78 90 80 92)(81 95 83 93)(82 94 84 96)
G:=sub<Sym(96)| (1,11,55)(2,12,56)(3,9,53)(4,10,54)(5,25,69)(6,26,70)(7,27,71)(8,28,72)(13,57,61)(14,58,62)(15,59,63)(16,60,64)(17,21,65)(18,22,66)(19,23,67)(20,24,68)(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)(45,52,93)(46,49,94)(47,50,95)(48,51,96), (1,59)(2,60)(3,57)(4,58)(5,21)(6,22)(7,23)(8,24)(9,61)(10,62)(11,63)(12,64)(13,53)(14,54)(15,55)(16,56)(17,69)(18,70)(19,71)(20,72)(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)(49,90)(50,91)(51,92)(52,89), (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), (1,75)(2,76)(3,73)(4,74)(5,52)(6,49)(7,50)(8,51)(9,77)(10,78)(11,79)(12,80)(13,81)(14,82)(15,83)(16,84)(17,85)(18,86)(19,87)(20,88)(21,89)(22,90)(23,91)(24,92)(25,93)(26,94)(27,95)(28,96)(29,53)(30,54)(31,55)(32,56)(33,57)(34,58)(35,59)(36,60)(37,61)(38,62)(39,63)(40,64)(41,65)(42,66)(43,67)(44,68)(45,69)(46,70)(47,71)(48,72), (1,4)(2,3)(5,51)(6,50)(7,49)(8,52)(9,12)(10,11)(13,14)(15,16)(17,86)(18,85)(19,88)(20,87)(21,90)(22,89)(23,92)(24,91)(25,96)(26,95)(27,94)(28,93)(29,32)(30,31)(33,34)(35,36)(37,38)(39,40)(41,66)(42,65)(43,68)(44,67)(45,72)(46,71)(47,70)(48,69)(53,56)(54,55)(57,58)(59,60)(61,62)(63,64)(73,76)(74,75)(77,80)(78,79)(81,82)(83,84), (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), (1,17,3,19)(2,20,4,18)(5,61,7,63)(6,64,8,62)(9,23,11,21)(10,22,12,24)(13,27,15,25)(14,26,16,28)(29,43,31,41)(30,42,32,44)(33,47,35,45)(34,46,36,48)(37,50,39,52)(38,49,40,51)(53,67,55,65)(54,66,56,68)(57,71,59,69)(58,70,60,72)(73,87,75,85)(74,86,76,88)(77,91,79,89)(78,90,80,92)(81,95,83,93)(82,94,84,96)>;
G:=Group( (1,11,55)(2,12,56)(3,9,53)(4,10,54)(5,25,69)(6,26,70)(7,27,71)(8,28,72)(13,57,61)(14,58,62)(15,59,63)(16,60,64)(17,21,65)(18,22,66)(19,23,67)(20,24,68)(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)(45,52,93)(46,49,94)(47,50,95)(48,51,96), (1,59)(2,60)(3,57)(4,58)(5,21)(6,22)(7,23)(8,24)(9,61)(10,62)(11,63)(12,64)(13,53)(14,54)(15,55)(16,56)(17,69)(18,70)(19,71)(20,72)(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)(49,90)(50,91)(51,92)(52,89), (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), (1,75)(2,76)(3,73)(4,74)(5,52)(6,49)(7,50)(8,51)(9,77)(10,78)(11,79)(12,80)(13,81)(14,82)(15,83)(16,84)(17,85)(18,86)(19,87)(20,88)(21,89)(22,90)(23,91)(24,92)(25,93)(26,94)(27,95)(28,96)(29,53)(30,54)(31,55)(32,56)(33,57)(34,58)(35,59)(36,60)(37,61)(38,62)(39,63)(40,64)(41,65)(42,66)(43,67)(44,68)(45,69)(46,70)(47,71)(48,72), (1,4)(2,3)(5,51)(6,50)(7,49)(8,52)(9,12)(10,11)(13,14)(15,16)(17,86)(18,85)(19,88)(20,87)(21,90)(22,89)(23,92)(24,91)(25,96)(26,95)(27,94)(28,93)(29,32)(30,31)(33,34)(35,36)(37,38)(39,40)(41,66)(42,65)(43,68)(44,67)(45,72)(46,71)(47,70)(48,69)(53,56)(54,55)(57,58)(59,60)(61,62)(63,64)(73,76)(74,75)(77,80)(78,79)(81,82)(83,84), (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), (1,17,3,19)(2,20,4,18)(5,61,7,63)(6,64,8,62)(9,23,11,21)(10,22,12,24)(13,27,15,25)(14,26,16,28)(29,43,31,41)(30,42,32,44)(33,47,35,45)(34,46,36,48)(37,50,39,52)(38,49,40,51)(53,67,55,65)(54,66,56,68)(57,71,59,69)(58,70,60,72)(73,87,75,85)(74,86,76,88)(77,91,79,89)(78,90,80,92)(81,95,83,93)(82,94,84,96) );
G=PermutationGroup([[(1,11,55),(2,12,56),(3,9,53),(4,10,54),(5,25,69),(6,26,70),(7,27,71),(8,28,72),(13,57,61),(14,58,62),(15,59,63),(16,60,64),(17,21,65),(18,22,66),(19,23,67),(20,24,68),(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),(45,52,93),(46,49,94),(47,50,95),(48,51,96)], [(1,59),(2,60),(3,57),(4,58),(5,21),(6,22),(7,23),(8,24),(9,61),(10,62),(11,63),(12,64),(13,53),(14,54),(15,55),(16,56),(17,69),(18,70),(19,71),(20,72),(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),(49,90),(50,91),(51,92),(52,89)], [(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)], [(1,75),(2,76),(3,73),(4,74),(5,52),(6,49),(7,50),(8,51),(9,77),(10,78),(11,79),(12,80),(13,81),(14,82),(15,83),(16,84),(17,85),(18,86),(19,87),(20,88),(21,89),(22,90),(23,91),(24,92),(25,93),(26,94),(27,95),(28,96),(29,53),(30,54),(31,55),(32,56),(33,57),(34,58),(35,59),(36,60),(37,61),(38,62),(39,63),(40,64),(41,65),(42,66),(43,67),(44,68),(45,69),(46,70),(47,71),(48,72)], [(1,4),(2,3),(5,51),(6,50),(7,49),(8,52),(9,12),(10,11),(13,14),(15,16),(17,86),(18,85),(19,88),(20,87),(21,90),(22,89),(23,92),(24,91),(25,96),(26,95),(27,94),(28,93),(29,32),(30,31),(33,34),(35,36),(37,38),(39,40),(41,66),(42,65),(43,68),(44,67),(45,72),(46,71),(47,70),(48,69),(53,56),(54,55),(57,58),(59,60),(61,62),(63,64),(73,76),(74,75),(77,80),(78,79),(81,82),(83,84)], [(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)], [(1,17,3,19),(2,20,4,18),(5,61,7,63),(6,64,8,62),(9,23,11,21),(10,22,12,24),(13,27,15,25),(14,26,16,28),(29,43,31,41),(30,42,32,44),(33,47,35,45),(34,46,36,48),(37,50,39,52),(38,49,40,51),(53,67,55,65),(54,66,56,68),(57,71,59,69),(58,70,60,72),(73,87,75,85),(74,86,76,88),(77,91,79,89),(78,90,80,92),(81,95,83,93),(82,94,84,96)]])
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 |
| type | + | + | + | + | + | + | + | + | + | - | ||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C3 | C6 | C6 | C6 | C6 | C6 | C6 | C6 | D4 | C3×D4 | 2- 1+4 | C3×2- 1+4 |
| kernel | C3×C23.38C23 | C3×C42⋊C2 | C3×C22⋊Q8 | C3×C22.D4 | C3×C4.4D4 | C3×C4⋊Q8 | Q8×C2×C6 | C6×C4○D4 | C23.38C23 | C42⋊C2 | C22⋊Q8 | C22.D4 | C4.4D4 | C4⋊Q8 | C22×Q8 | C2×C4○D4 | C2×C12 | C2×C4 | C6 | C2 |
| # reps | 1 | 1 | 4 | 4 | 2 | 2 | 1 | 1 | 2 | 2 | 8 | 8 | 4 | 4 | 2 | 2 | 4 | 8 | 2 | 4 |
Matrix representation of C3×C23.38C23 ►in GL6(𝔽13)
| 9 | 0 | 0 | 0 | 0 | 0 |
| 0 | 9 | 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 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 12 | 12 | 12 | 11 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 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 | 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 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 1 | 1 | 2 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 12 | 12 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 12 | 12 | 12 | 11 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 0 | 0 | 0 |
| 0 | 0 | 0 | 5 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 0 |
| 0 | 0 | 8 | 8 | 0 | 8 |
G:=sub<GL(6,GF(13))| [9,0,0,0,0,0,0,9,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,12,0,0,0,1,0,12,0,0,0,0,0,12,0,0,0,0,0,11,1],[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],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[12,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,12,0,0,0,1,0,0,0,0,1,1,0,12,0,0,0,2,0,12],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,12,12,1,0,0,0,12,0,1,0,0,1,12,0,0,0,0,0,11,0,1],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,5,0,0,8,0,0,0,5,0,8,0,0,0,0,8,0,0,0,0,0,0,8] >;
C3×C23.38C23 in GAP, Magma, Sage, TeX
C_3\times C_2^3._{38}C_2^3 % in TeX
G:=Group("C3xC2^3.38C2^3"); // GroupNames label
G:=SmallGroup(192,1425);
// by ID
G=gap.SmallGroup(192,1425);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-2,-2,701,344,2102,555,268,1571]);
// Polycyclic
G:=Group<a,b,c,d,e,f,g|a^3=b^2=c^2=d^2=e^2=1,f^2=g^2=c,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,a*g=g*a,e*b*e=b*c=c*b,b*d=d*b,b*f=f*b,b*g=g*b,c*d=d*c,f*e*f^-1=c*e=e*c,g*f*g^-1=c*f=f*c,c*g=g*c,g*e*g^-1=d*e=e*d,d*f=f*d,d*g=g*d>;
// generators/relations