direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C3×C23.36C23, (C4×D4)⋊8C6, (C4×Q8)⋊11C6, (D4×C12)⋊37C2, (C2×C42)⋊13C6, (Q8×C12)⋊27C2, C22⋊Q8⋊22C6, C42⋊C2⋊9C6, C4.4D4⋊17C6, C4⋊D4.10C6, C42.34(C2×C6), C42.C2⋊13C6, C42⋊2C2⋊12C6, (C2×C6).349C24, C23.7(C22×C6), C12.274(C4○D4), (C2×C12).960C23, (C4×C12).373C22, (C6×D4).318C22, C22.D4⋊16C6, C22.23(C23×C6), (C22×C6).87C23, (C6×Q8).266C22, (C22×C12).511C22, (C2×C4×C12)⋊23C2, C4⋊C4.64(C2×C6), C2.12(C6×C4○D4), C4.56(C3×C4○D4), (C2×D4).63(C2×C6), C6.231(C2×C4○D4), (C3×C22⋊Q8)⋊49C2, (C2×Q8).65(C2×C6), C22.3(C3×C4○D4), (C2×C6).51(C4○D4), (C3×C4⋊D4).20C2, (C3×C4.4D4)⋊37C2, C22⋊C4.12(C2×C6), (C22×C4).59(C2×C6), (C2×C4).17(C22×C6), (C3×C42.C2)⋊30C2, (C3×C42⋊2C2)⋊21C2, (C3×C42⋊C2)⋊30C2, (C3×C4⋊C4).387C22, (C3×C22.D4)⋊35C2, (C3×C22⋊C4).146C22, SmallGroup(192,1418)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 322 in 234 conjugacy classes, 154 normal (62 characteristic)
C1, C2 [×3], C2 [×4], C3, C4 [×4], C4 [×10], C22, C22 [×2], C22 [×8], C6 [×3], C6 [×4], C2×C4 [×6], C2×C4 [×6], C2×C4 [×10], D4 [×6], Q8 [×2], C23, C23 [×2], C12 [×4], C12 [×10], C2×C6, C2×C6 [×2], C2×C6 [×8], C42 [×4], C42 [×2], C22⋊C4 [×10], C4⋊C4 [×2], C4⋊C4 [×8], C22×C4 [×3], C22×C4 [×2], C2×D4, C2×D4 [×2], C2×Q8, C2×C12 [×6], C2×C12 [×6], C2×C12 [×10], C3×D4 [×6], C3×Q8 [×2], C22×C6, C22×C6 [×2], C2×C42, C42⋊C2 [×2], C4×D4, C4×D4 [×2], C4×Q8, C4⋊D4, C22⋊Q8, C22.D4 [×2], C4.4D4, C42.C2, C42⋊2C2 [×2], C4×C12 [×4], C4×C12 [×2], C3×C22⋊C4 [×10], C3×C4⋊C4 [×2], C3×C4⋊C4 [×8], C22×C12 [×3], C22×C12 [×2], C6×D4, C6×D4 [×2], C6×Q8, C23.36C23, C2×C4×C12, C3×C42⋊C2 [×2], D4×C12, D4×C12 [×2], Q8×C12, C3×C4⋊D4, C3×C22⋊Q8, C3×C22.D4 [×2], C3×C4.4D4, C3×C42.C2, C3×C42⋊2C2 [×2], C3×C23.36C23
Quotients:
C1, C2 [×15], C3, C22 [×35], C6 [×15], C23 [×15], C2×C6 [×35], C4○D4 [×6], C24, C22×C6 [×15], C2×C4○D4 [×3], C3×C4○D4 [×6], C23×C6, C23.36C23, C6×C4○D4 [×3], C3×C23.36C23
Generators and relations
G = < a,b,c,d,e,f,g | a3=b2=c2=d2=e2=1, f2=d, g2=c, ab=ba, ac=ca, ad=da, ae=ea, af=fa, ag=ga, bc=cb, ebe=bd=db, bf=fb, bg=gb, cd=dc, fef-1=ce=ec, cf=fc, cg=gc, de=ed, df=fd, dg=gd, eg=ge, fg=gf >
►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 65)(2 66)(3 67)(4 68)(5 64)(6 61)(7 62)(8 63)(9 21)(10 22)(11 23)(12 24)(13 25)(14 26)(15 27)(16 28)(17 55)(18 56)(19 53)(20 54)(29 41)(30 42)(31 43)(32 44)(33 45)(34 46)(35 47)(36 48)(37 51)(38 52)(39 49)(40 50)(57 69)(58 70)(59 71)(60 72)(73 85)(74 86)(75 87)(76 88)(77 89)(78 90)(79 91)(80 92)(81 93)(82 94)(83 95)(84 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)
(1 28)(2 47)(3 26)(4 45)(5 9)(6 32)(7 11)(8 30)(10 95)(12 93)(13 86)(14 65)(15 88)(16 67)(17 90)(18 69)(19 92)(20 71)(21 62)(22 81)(23 64)(24 83)(25 76)(27 74)(29 96)(31 94)(33 66)(34 85)(35 68)(36 87)(37 70)(38 89)(39 72)(40 91)(41 82)(42 61)(43 84)(44 63)(46 75)(48 73)(49 58)(50 77)(51 60)(52 79)(53 78)(54 57)(55 80)(56 59)
(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 35 75 13)(2 36 76 14)(3 33 73 15)(4 34 74 16)(5 24 94 42)(6 21 95 43)(7 22 96 44)(8 23 93 41)(9 83 31 61)(10 84 32 62)(11 81 29 63)(12 82 30 64)(17 57 39 79)(18 58 40 80)(19 59 37 77)(20 60 38 78)(25 65 47 87)(26 66 48 88)(27 67 45 85)(28 68 46 86)(49 91 55 69)(50 92 56 70)(51 89 53 71)(52 90 54 72)
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), (1,65)(2,66)(3,67)(4,68)(5,64)(6,61)(7,62)(8,63)(9,21)(10,22)(11,23)(12,24)(13,25)(14,26)(15,27)(16,28)(17,55)(18,56)(19,53)(20,54)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)(37,51)(38,52)(39,49)(40,50)(57,69)(58,70)(59,71)(60,72)(73,85)(74,86)(75,87)(76,88)(77,89)(78,90)(79,91)(80,92)(81,93)(82,94)(83,95)(84,96), (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), (1,28)(2,47)(3,26)(4,45)(5,9)(6,32)(7,11)(8,30)(10,95)(12,93)(13,86)(14,65)(15,88)(16,67)(17,90)(18,69)(19,92)(20,71)(21,62)(22,81)(23,64)(24,83)(25,76)(27,74)(29,96)(31,94)(33,66)(34,85)(35,68)(36,87)(37,70)(38,89)(39,72)(40,91)(41,82)(42,61)(43,84)(44,63)(46,75)(48,73)(49,58)(50,77)(51,60)(52,79)(53,78)(54,57)(55,80)(56,59), (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), (1,35,75,13)(2,36,76,14)(3,33,73,15)(4,34,74,16)(5,24,94,42)(6,21,95,43)(7,22,96,44)(8,23,93,41)(9,83,31,61)(10,84,32,62)(11,81,29,63)(12,82,30,64)(17,57,39,79)(18,58,40,80)(19,59,37,77)(20,60,38,78)(25,65,47,87)(26,66,48,88)(27,67,45,85)(28,68,46,86)(49,91,55,69)(50,92,56,70)(51,89,53,71)(52,90,54,72)>;
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), (1,65)(2,66)(3,67)(4,68)(5,64)(6,61)(7,62)(8,63)(9,21)(10,22)(11,23)(12,24)(13,25)(14,26)(15,27)(16,28)(17,55)(18,56)(19,53)(20,54)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)(37,51)(38,52)(39,49)(40,50)(57,69)(58,70)(59,71)(60,72)(73,85)(74,86)(75,87)(76,88)(77,89)(78,90)(79,91)(80,92)(81,93)(82,94)(83,95)(84,96), (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), (1,28)(2,47)(3,26)(4,45)(5,9)(6,32)(7,11)(8,30)(10,95)(12,93)(13,86)(14,65)(15,88)(16,67)(17,90)(18,69)(19,92)(20,71)(21,62)(22,81)(23,64)(24,83)(25,76)(27,74)(29,96)(31,94)(33,66)(34,85)(35,68)(36,87)(37,70)(38,89)(39,72)(40,91)(41,82)(42,61)(43,84)(44,63)(46,75)(48,73)(49,58)(50,77)(51,60)(52,79)(53,78)(54,57)(55,80)(56,59), (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), (1,35,75,13)(2,36,76,14)(3,33,73,15)(4,34,74,16)(5,24,94,42)(6,21,95,43)(7,22,96,44)(8,23,93,41)(9,83,31,61)(10,84,32,62)(11,81,29,63)(12,82,30,64)(17,57,39,79)(18,58,40,80)(19,59,37,77)(20,60,38,78)(25,65,47,87)(26,66,48,88)(27,67,45,85)(28,68,46,86)(49,91,55,69)(50,92,56,70)(51,89,53,71)(52,90,54,72) );
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)], [(1,65),(2,66),(3,67),(4,68),(5,64),(6,61),(7,62),(8,63),(9,21),(10,22),(11,23),(12,24),(13,25),(14,26),(15,27),(16,28),(17,55),(18,56),(19,53),(20,54),(29,41),(30,42),(31,43),(32,44),(33,45),(34,46),(35,47),(36,48),(37,51),(38,52),(39,49),(40,50),(57,69),(58,70),(59,71),(60,72),(73,85),(74,86),(75,87),(76,88),(77,89),(78,90),(79,91),(80,92),(81,93),(82,94),(83,95),(84,96)], [(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)], [(1,28),(2,47),(3,26),(4,45),(5,9),(6,32),(7,11),(8,30),(10,95),(12,93),(13,86),(14,65),(15,88),(16,67),(17,90),(18,69),(19,92),(20,71),(21,62),(22,81),(23,64),(24,83),(25,76),(27,74),(29,96),(31,94),(33,66),(34,85),(35,68),(36,87),(37,70),(38,89),(39,72),(40,91),(41,82),(42,61),(43,84),(44,63),(46,75),(48,73),(49,58),(50,77),(51,60),(52,79),(53,78),(54,57),(55,80),(56,59)], [(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)], [(1,35,75,13),(2,36,76,14),(3,33,73,15),(4,34,74,16),(5,24,94,42),(6,21,95,43),(7,22,96,44),(8,23,93,41),(9,83,31,61),(10,84,32,62),(11,81,29,63),(12,82,30,64),(17,57,39,79),(18,58,40,80),(19,59,37,77),(20,60,38,78),(25,65,47,87),(26,66,48,88),(27,67,45,85),(28,68,46,86),(49,91,55,69),(50,92,56,70),(51,89,53,71),(52,90,54,72)])
Matrix representation ►G ⊆ GL4(𝔽13) generated by
| 9 | 0 | 0 | 0 |
| 0 | 9 | 0 | 0 |
| 0 | 0 | 3 | 0 |
| 0 | 0 | 0 | 3 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
| 12 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 12 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 12 |
| 1 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 8 |
| 0 | 0 | 5 | 0 |
| 0 | 8 | 0 | 0 |
| 8 | 0 | 0 | 0 |
| 0 | 0 | 8 | 0 |
| 0 | 0 | 0 | 8 |
| 5 | 0 | 0 | 0 |
| 0 | 5 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
G:=sub<GL(4,GF(13))| [9,0,0,0,0,9,0,0,0,0,3,0,0,0,0,3],[0,1,0,0,1,0,0,0,0,0,0,1,0,0,1,0],[12,0,0,0,0,12,0,0,0,0,1,0,0,0,0,1],[12,0,0,0,0,12,0,0,0,0,12,0,0,0,0,12],[1,0,0,0,0,12,0,0,0,0,0,5,0,0,8,0],[0,8,0,0,8,0,0,0,0,0,8,0,0,0,0,8],[5,0,0,0,0,5,0,0,0,0,1,0,0,0,0,1] >;
84 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3A | 3B | 4A | 4B | 4C | 4D | 4E | ··· | 4N | 4O | ··· | 4T | 6A | ··· | 6F | 6G | 6H | 6I | 6J | 6K | 6L | 6M | 6N | 12A | ··· | 12H | 12I | ··· | 12AB | 12AC | ··· | 12AN |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 6 | ··· | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 12 | ··· | 12 | 12 | ··· | 12 | 12 | ··· | 12 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 |
84 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | + | |||||||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C3 | C6 | C6 | C6 | C6 | C6 | C6 | C6 | C6 | C6 | C6 | C4○D4 | C4○D4 | C3×C4○D4 | C3×C4○D4 |
| kernel | C3×C23.36C23 | C2×C4×C12 | C3×C42⋊C2 | D4×C12 | Q8×C12 | C3×C4⋊D4 | C3×C22⋊Q8 | C3×C22.D4 | C3×C4.4D4 | C3×C42.C2 | C3×C42⋊2C2 | C23.36C23 | C2×C42 | C42⋊C2 | C4×D4 | C4×Q8 | C4⋊D4 | C22⋊Q8 | C22.D4 | C4.4D4 | C42.C2 | C42⋊2C2 | C12 | C2×C6 | C4 | C22 |
| # reps | 1 | 1 | 2 | 3 | 1 | 1 | 1 | 2 | 1 | 1 | 2 | 2 | 2 | 4 | 6 | 2 | 2 | 2 | 4 | 2 | 2 | 4 | 8 | 4 | 16 | 8 |
In GAP, Magma, Sage, TeX
C_3\times C_2^3._{36}C_2^3 % in TeX
G:=Group("C3xC2^3.36C2^3"); // GroupNames label
G:=SmallGroup(192,1418);
// by ID
G=gap.SmallGroup(192,1418);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-2,-2,701,680,2102,192]);
// Polycyclic
G:=Group<a,b,c,d,e,f,g|a^3=b^2=c^2=d^2=e^2=1,f^2=d,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,b*c=c*b,e*b*e=b*d=d*b,b*f=f*b,b*g=g*b,c*d=d*c,f*e*f^-1=c*e=e*c,c*f=f*c,c*g=g*c,d*e=e*d,d*f=f*d,d*g=g*d,e*g=g*e,f*g=g*f>;
// generators/relations
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