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G = C4×D23order 184 = 23·23

Direct product of C4 and D23

direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary

Aliases: C4×D23, C922C2, D46.C2, C2.1D46, Dic232C2, C46.2C22, C231(C2×C4), SmallGroup(184,4)

Series: Derived Chief Lower central Upper central

C1C23 — C4×D23
C1C23C46D46 — C4×D23
C23 — C4×D23
C1C4

Generators and relations for C4×D23
 G = < a,b,c | a4=b23=c2=1, ab=ba, ac=ca, cbc=b-1 >

23C2
23C2
23C22
23C4
23C2×C4

Smallest permutation representation of C4×D23
On 92 points
Generators in S92
(1 72 29 67)(2 73 30 68)(3 74 31 69)(4 75 32 47)(5 76 33 48)(6 77 34 49)(7 78 35 50)(8 79 36 51)(9 80 37 52)(10 81 38 53)(11 82 39 54)(12 83 40 55)(13 84 41 56)(14 85 42 57)(15 86 43 58)(16 87 44 59)(17 88 45 60)(18 89 46 61)(19 90 24 62)(20 91 25 63)(21 92 26 64)(22 70 27 65)(23 71 28 66)
(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)
(1 23)(2 22)(3 21)(4 20)(5 19)(6 18)(7 17)(8 16)(9 15)(10 14)(11 13)(24 33)(25 32)(26 31)(27 30)(28 29)(34 46)(35 45)(36 44)(37 43)(38 42)(39 41)(47 63)(48 62)(49 61)(50 60)(51 59)(52 58)(53 57)(54 56)(64 69)(65 68)(66 67)(70 73)(71 72)(74 92)(75 91)(76 90)(77 89)(78 88)(79 87)(80 86)(81 85)(82 84)

G:=sub<Sym(92)| (1,72,29,67)(2,73,30,68)(3,74,31,69)(4,75,32,47)(5,76,33,48)(6,77,34,49)(7,78,35,50)(8,79,36,51)(9,80,37,52)(10,81,38,53)(11,82,39,54)(12,83,40,55)(13,84,41,56)(14,85,42,57)(15,86,43,58)(16,87,44,59)(17,88,45,60)(18,89,46,61)(19,90,24,62)(20,91,25,63)(21,92,26,64)(22,70,27,65)(23,71,28,66), (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), (1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)(24,33)(25,32)(26,31)(27,30)(28,29)(34,46)(35,45)(36,44)(37,43)(38,42)(39,41)(47,63)(48,62)(49,61)(50,60)(51,59)(52,58)(53,57)(54,56)(64,69)(65,68)(66,67)(70,73)(71,72)(74,92)(75,91)(76,90)(77,89)(78,88)(79,87)(80,86)(81,85)(82,84)>;

G:=Group( (1,72,29,67)(2,73,30,68)(3,74,31,69)(4,75,32,47)(5,76,33,48)(6,77,34,49)(7,78,35,50)(8,79,36,51)(9,80,37,52)(10,81,38,53)(11,82,39,54)(12,83,40,55)(13,84,41,56)(14,85,42,57)(15,86,43,58)(16,87,44,59)(17,88,45,60)(18,89,46,61)(19,90,24,62)(20,91,25,63)(21,92,26,64)(22,70,27,65)(23,71,28,66), (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), (1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)(24,33)(25,32)(26,31)(27,30)(28,29)(34,46)(35,45)(36,44)(37,43)(38,42)(39,41)(47,63)(48,62)(49,61)(50,60)(51,59)(52,58)(53,57)(54,56)(64,69)(65,68)(66,67)(70,73)(71,72)(74,92)(75,91)(76,90)(77,89)(78,88)(79,87)(80,86)(81,85)(82,84) );

G=PermutationGroup([(1,72,29,67),(2,73,30,68),(3,74,31,69),(4,75,32,47),(5,76,33,48),(6,77,34,49),(7,78,35,50),(8,79,36,51),(9,80,37,52),(10,81,38,53),(11,82,39,54),(12,83,40,55),(13,84,41,56),(14,85,42,57),(15,86,43,58),(16,87,44,59),(17,88,45,60),(18,89,46,61),(19,90,24,62),(20,91,25,63),(21,92,26,64),(22,70,27,65),(23,71,28,66)], [(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)], [(1,23),(2,22),(3,21),(4,20),(5,19),(6,18),(7,17),(8,16),(9,15),(10,14),(11,13),(24,33),(25,32),(26,31),(27,30),(28,29),(34,46),(35,45),(36,44),(37,43),(38,42),(39,41),(47,63),(48,62),(49,61),(50,60),(51,59),(52,58),(53,57),(54,56),(64,69),(65,68),(66,67),(70,73),(71,72),(74,92),(75,91),(76,90),(77,89),(78,88),(79,87),(80,86),(81,85),(82,84)])

C4×D23 is a maximal subgroup of   C8⋊D23  D925C2  D42D23  D92⋊C2
C4×D23 is a maximal quotient of   C8⋊D23  Dic23⋊C4  D46⋊C4

52 conjugacy classes

class 1 2A2B2C4A4B4C4D23A···23K46A···46K92A···92V
order1222444423···2346···4692···92
size1123231123232···22···22···2

52 irreducible representations

dim11111222
type++++++
imageC1C2C2C2C4D23D46C4×D23
kernelC4×D23Dic23C92D46D23C4C2C1
# reps11114111122

Matrix representation of C4×D23 in GL2(𝔽277) generated by

2170
0217
,
01
27657
,
01
10
G:=sub<GL(2,GF(277))| [217,0,0,217],[0,276,1,57],[0,1,1,0] >;

C4×D23 in GAP, Magma, Sage, TeX

C_4\times D_{23}
% in TeX

G:=Group("C4xD23");
// GroupNames label

G:=SmallGroup(184,4);
// by ID

G=gap.SmallGroup(184,4);
# by ID

G:=PCGroup([4,-2,-2,-2,-23,21,2819]);
// Polycyclic

G:=Group<a,b,c|a^4=b^23=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C4×D23 in TeX

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