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## G = C2×He3⋊3D4order 432 = 24·33

### Direct product of C2 and He3⋊3D4

Series: Derived Chief Lower central Upper central

 Derived series C1 — C3 — C2×He3 — C2×He3⋊3D4
 Chief series C1 — C3 — C32 — He3 — C2×He3 — C2×C32⋊C6 — He3⋊3D4 — C2×He3⋊3D4
 Lower central He3 — C2×He3 — C2×He3⋊3D4
 Upper central C1 — C22

Generators and relations for C2×He33D4
G = < a,b,c,d,e,f | a2=b3=c3=d3=e4=f2=1, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, dbd-1=bc-1, be=eb, fbf=b-1, cd=dc, ece-1=c-1, cf=fc, ede-1=fdf=d-1, fef=e-1 >

Subgroups: 1363 in 221 conjugacy classes, 45 normal (21 characteristic)
C1, C2, C2, C2, C3, C3, C4, C22, C22, S3, C6, C6, C6, C2×C4, D4, C23, C32, C32, Dic3, C12, D6, C2×C6, C2×C6, C2×D4, C3×S3, C3⋊S3, C3×C6, C3×C6, C3×C6, D12, C2×Dic3, C3⋊D4, C2×C12, C22×S3, C22×C6, He3, C3×Dic3, C3⋊Dic3, S3×C6, C2×C3⋊S3, C2×C3⋊S3, C62, C62, C2×D12, C2×C3⋊D4, C32⋊C6, He3⋊C2, C2×He3, C2×He3, D6⋊S3, C3⋊D12, C6×Dic3, C2×C3⋊Dic3, S3×C2×C6, C22×C3⋊S3, C32⋊C12, C2×C32⋊C6, C2×C32⋊C6, C2×He3⋊C2, C2×He3⋊C2, C22×He3, C2×D6⋊S3, C2×C3⋊D12, He33D4, C2×C32⋊C12, C22×C32⋊C6, C22×He3⋊C2, C2×He33D4
Quotients: C1, C2, C22, S3, D4, C23, D6, C2×D4, D12, C3⋊D4, C22×S3, S32, C2×D12, C2×C3⋊D4, C3⋊D12, C2×S32, C32⋊D6, C2×C3⋊D12, He33D4, C2×C32⋊D6, C2×He33D4

Smallest permutation representation of C2×He33D4
On 72 points
Generators in S72
(1 41)(2 42)(3 43)(4 44)(5 23)(6 24)(7 21)(8 22)(9 36)(10 33)(11 34)(12 35)(13 37)(14 38)(15 39)(16 40)(17 46)(18 47)(19 48)(20 45)(25 69)(26 70)(27 71)(28 72)(29 68)(30 65)(31 66)(32 67)(49 62)(50 63)(51 64)(52 61)(53 59)(54 60)(55 57)(56 58)
(1 24 32)(2 21 29)(3 22 30)(4 23 31)(5 66 44)(6 67 41)(7 68 42)(8 65 43)(9 54 19)(10 55 20)(11 56 17)(12 53 18)(13 25 50)(14 26 51)(15 27 52)(16 28 49)(33 57 45)(34 58 46)(35 59 47)(36 60 48)(37 69 63)(38 70 64)(39 71 61)(40 72 62)
(1 19 37)(2 38 20)(3 17 39)(4 40 18)(5 28 35)(6 36 25)(7 26 33)(8 34 27)(9 69 24)(10 21 70)(11 71 22)(12 23 72)(13 41 48)(14 45 42)(15 43 46)(16 47 44)(29 64 55)(30 56 61)(31 62 53)(32 54 63)(49 59 66)(50 67 60)(51 57 68)(52 65 58)
(5 28 35)(6 36 25)(7 26 33)(8 34 27)(9 69 24)(10 21 70)(11 71 22)(12 23 72)(29 55 64)(30 61 56)(31 53 62)(32 63 54)(49 66 59)(50 60 67)(51 68 57)(52 58 65)
(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)
(1 3)(5 66)(6 65)(7 68)(8 67)(9 56)(10 55)(11 54)(12 53)(13 15)(17 19)(21 29)(22 32)(23 31)(24 30)(25 52)(26 51)(27 50)(28 49)(33 57)(34 60)(35 59)(36 58)(37 39)(41 43)(46 48)(61 69)(62 72)(63 71)(64 70)

G:=sub<Sym(72)| (1,41)(2,42)(3,43)(4,44)(5,23)(6,24)(7,21)(8,22)(9,36)(10,33)(11,34)(12,35)(13,37)(14,38)(15,39)(16,40)(17,46)(18,47)(19,48)(20,45)(25,69)(26,70)(27,71)(28,72)(29,68)(30,65)(31,66)(32,67)(49,62)(50,63)(51,64)(52,61)(53,59)(54,60)(55,57)(56,58), (1,24,32)(2,21,29)(3,22,30)(4,23,31)(5,66,44)(6,67,41)(7,68,42)(8,65,43)(9,54,19)(10,55,20)(11,56,17)(12,53,18)(13,25,50)(14,26,51)(15,27,52)(16,28,49)(33,57,45)(34,58,46)(35,59,47)(36,60,48)(37,69,63)(38,70,64)(39,71,61)(40,72,62), (1,19,37)(2,38,20)(3,17,39)(4,40,18)(5,28,35)(6,36,25)(7,26,33)(8,34,27)(9,69,24)(10,21,70)(11,71,22)(12,23,72)(13,41,48)(14,45,42)(15,43,46)(16,47,44)(29,64,55)(30,56,61)(31,62,53)(32,54,63)(49,59,66)(50,67,60)(51,57,68)(52,65,58), (5,28,35)(6,36,25)(7,26,33)(8,34,27)(9,69,24)(10,21,70)(11,71,22)(12,23,72)(29,55,64)(30,61,56)(31,53,62)(32,63,54)(49,66,59)(50,60,67)(51,68,57)(52,58,65), (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), (1,3)(5,66)(6,65)(7,68)(8,67)(9,56)(10,55)(11,54)(12,53)(13,15)(17,19)(21,29)(22,32)(23,31)(24,30)(25,52)(26,51)(27,50)(28,49)(33,57)(34,60)(35,59)(36,58)(37,39)(41,43)(46,48)(61,69)(62,72)(63,71)(64,70)>;

G:=Group( (1,41)(2,42)(3,43)(4,44)(5,23)(6,24)(7,21)(8,22)(9,36)(10,33)(11,34)(12,35)(13,37)(14,38)(15,39)(16,40)(17,46)(18,47)(19,48)(20,45)(25,69)(26,70)(27,71)(28,72)(29,68)(30,65)(31,66)(32,67)(49,62)(50,63)(51,64)(52,61)(53,59)(54,60)(55,57)(56,58), (1,24,32)(2,21,29)(3,22,30)(4,23,31)(5,66,44)(6,67,41)(7,68,42)(8,65,43)(9,54,19)(10,55,20)(11,56,17)(12,53,18)(13,25,50)(14,26,51)(15,27,52)(16,28,49)(33,57,45)(34,58,46)(35,59,47)(36,60,48)(37,69,63)(38,70,64)(39,71,61)(40,72,62), (1,19,37)(2,38,20)(3,17,39)(4,40,18)(5,28,35)(6,36,25)(7,26,33)(8,34,27)(9,69,24)(10,21,70)(11,71,22)(12,23,72)(13,41,48)(14,45,42)(15,43,46)(16,47,44)(29,64,55)(30,56,61)(31,62,53)(32,54,63)(49,59,66)(50,67,60)(51,57,68)(52,65,58), (5,28,35)(6,36,25)(7,26,33)(8,34,27)(9,69,24)(10,21,70)(11,71,22)(12,23,72)(29,55,64)(30,61,56)(31,53,62)(32,63,54)(49,66,59)(50,60,67)(51,68,57)(52,58,65), (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), (1,3)(5,66)(6,65)(7,68)(8,67)(9,56)(10,55)(11,54)(12,53)(13,15)(17,19)(21,29)(22,32)(23,31)(24,30)(25,52)(26,51)(27,50)(28,49)(33,57)(34,60)(35,59)(36,58)(37,39)(41,43)(46,48)(61,69)(62,72)(63,71)(64,70) );

G=PermutationGroup([[(1,41),(2,42),(3,43),(4,44),(5,23),(6,24),(7,21),(8,22),(9,36),(10,33),(11,34),(12,35),(13,37),(14,38),(15,39),(16,40),(17,46),(18,47),(19,48),(20,45),(25,69),(26,70),(27,71),(28,72),(29,68),(30,65),(31,66),(32,67),(49,62),(50,63),(51,64),(52,61),(53,59),(54,60),(55,57),(56,58)], [(1,24,32),(2,21,29),(3,22,30),(4,23,31),(5,66,44),(6,67,41),(7,68,42),(8,65,43),(9,54,19),(10,55,20),(11,56,17),(12,53,18),(13,25,50),(14,26,51),(15,27,52),(16,28,49),(33,57,45),(34,58,46),(35,59,47),(36,60,48),(37,69,63),(38,70,64),(39,71,61),(40,72,62)], [(1,19,37),(2,38,20),(3,17,39),(4,40,18),(5,28,35),(6,36,25),(7,26,33),(8,34,27),(9,69,24),(10,21,70),(11,71,22),(12,23,72),(13,41,48),(14,45,42),(15,43,46),(16,47,44),(29,64,55),(30,56,61),(31,62,53),(32,54,63),(49,59,66),(50,67,60),(51,57,68),(52,65,58)], [(5,28,35),(6,36,25),(7,26,33),(8,34,27),(9,69,24),(10,21,70),(11,71,22),(12,23,72),(29,55,64),(30,61,56),(31,53,62),(32,63,54),(49,66,59),(50,60,67),(51,68,57),(52,58,65)], [(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)], [(1,3),(5,66),(6,65),(7,68),(8,67),(9,56),(10,55),(11,54),(12,53),(13,15),(17,19),(21,29),(22,32),(23,31),(24,30),(25,52),(26,51),(27,50),(28,49),(33,57),(34,60),(35,59),(36,58),(37,39),(41,43),(46,48),(61,69),(62,72),(63,71),(64,70)]])

38 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 2G 3A 3B 3C 3D 4A 4B 6A 6B 6C 6D ··· 6I 6J 6K 6L 6M ··· 6T 12A 12B 12C 12D order 1 2 2 2 2 2 2 2 3 3 3 3 4 4 6 6 6 6 ··· 6 6 6 6 6 ··· 6 12 12 12 12 size 1 1 1 1 18 18 18 18 2 6 6 12 18 18 2 2 2 6 ··· 6 12 12 12 18 ··· 18 18 18 18 18

38 irreducible representations

 dim 1 1 1 1 1 2 2 2 2 2 2 2 2 4 4 4 6 6 6 type + + + + + + + + + + + + + + + + + image C1 C2 C2 C2 C2 S3 S3 D4 D6 D6 D6 D12 C3⋊D4 S32 C3⋊D12 C2×S32 C32⋊D6 He3⋊3D4 C2×C32⋊D6 kernel C2×He3⋊3D4 He3⋊3D4 C2×C32⋊C12 C22×C32⋊C6 C22×He3⋊C2 C2×C3⋊Dic3 C22×C3⋊S3 C2×He3 C3⋊Dic3 C2×C3⋊S3 C62 C3×C6 C3×C6 C2×C6 C6 C6 C22 C2 C2 # reps 1 4 1 1 1 1 1 2 2 2 2 4 4 1 2 1 2 4 2

Matrix representation of C2×He33D4 in GL14(𝔽13)

 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
,
 12 0 12 0 0 0 0 0 0 0 0 0 0 0 0 12 0 12 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 12 0 0 0 0 0 0 0 0 0 0 0 0 12 0 12 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
,
 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 1 12
,
 0 12 0 0 0 0 0 0 0 0 0 0 0 0 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 1 0 0 0 0 0 0 0 0 0 0 0 0 12 0
,
 0 10 0 7 0 0 0 0 0 0 0 0 0 0 10 0 7 0 0 0 0 0 0 0 0 0 0 0 0 6 0 3 0 0 0 0 0 0 0 0 0 0 6 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 7 0 0 0 0 0 0 0 0 0 0 10 0 7 0 0 0 0 0 0 0 0 0 0 0 0 6 0 3 0 0 0 0 0 0 0 0 0 0 6 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 12 0
,
 0 12 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0

G:=sub<GL(14,GF(13))| [12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],[12,0,1,0,0,0,0,0,0,0,0,0,0,0,0,12,0,1,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,1,0,0,0,0,0,0,0,0,0,0,0,0,12,0,1,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,12,12],[0,1,0,0,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,12,0,0,0,0,0,0,0,0,0,0,0,0,1,0],[0,10,0,6,0,0,0,0,0,0,0,0,0,0,10,0,6,0,0,0,0,0,0,0,0,0,0,0,0,7,0,3,0,0,0,0,0,0,0,0,0,0,7,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10,0,6,0,0,0,0,0,0,0,0,0,0,10,0,6,0,0,0,0,0,0,0,0,0,0,0,0,7,0,3,0,0,0,0,0,0,0,0,0,0,7,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,12,0],[0,12,0,1,0,0,0,0,0,0,0,0,0,0,12,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,1,0,0,0,0,0,0,0,0,0,0,12,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0] >;

C2×He33D4 in GAP, Magma, Sage, TeX

C_2\times {\rm He}_3\rtimes_3D_4
% in TeX

G:=Group("C2xHe3:3D4");
// GroupNames label

G:=SmallGroup(432,322);
// by ID

G=gap.SmallGroup(432,322);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,141,64,571,4037,537,14118,7069]);
// Polycyclic

G:=Group<a,b,c,d,e,f|a^2=b^3=c^3=d^3=e^4=f^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,d*b*d^-1=b*c^-1,b*e=e*b,f*b*f=b^-1,c*d=d*c,e*c*e^-1=c^-1,c*f=f*c,e*d*e^-1=f*d*f=d^-1,f*e*f=e^-1>;
// generators/relations

׿
×
𝔽