Copied to
clipboard

G = C2×C46order 92 = 22·23

Abelian group of type [2,46]

direct product, abelian, monomial, 2-elementary

Aliases: C2×C46, SmallGroup(92,4)

Series: Derived Chief Lower central Upper central

C1 — C2×C46
C1C23C46 — C2×C46
C1 — C2×C46
C1 — C2×C46

Generators and relations for C2×C46
 G = < a,b | a2=b46=1, ab=ba >


Smallest permutation representation of C2×C46
Regular action on 92 points
Generators in S92
(1 77)(2 78)(3 79)(4 80)(5 81)(6 82)(7 83)(8 84)(9 85)(10 86)(11 87)(12 88)(13 89)(14 90)(15 91)(16 92)(17 47)(18 48)(19 49)(20 50)(21 51)(22 52)(23 53)(24 54)(25 55)(26 56)(27 57)(28 58)(29 59)(30 60)(31 61)(32 62)(33 63)(34 64)(35 65)(36 66)(37 67)(38 68)(39 69)(40 70)(41 71)(42 72)(43 73)(44 74)(45 75)(46 76)
(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)

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

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

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

C2×C46 is a maximal subgroup of   C23⋊D4

92 conjugacy classes

class 1 2A2B2C23A···23V46A···46BN
order122223···2346···46
size11111···11···1

92 irreducible representations

dim1111
type++
imageC1C2C23C46
kernelC2×C46C46C22C2
# reps132266

Matrix representation of C2×C46 in GL2(𝔽47) generated by

460
01
,
170
05
G:=sub<GL(2,GF(47))| [46,0,0,1],[17,0,0,5] >;

C2×C46 in GAP, Magma, Sage, TeX

C_2\times C_{46}
% in TeX

G:=Group("C2xC46");
// GroupNames label

G:=SmallGroup(92,4);
// by ID

G=gap.SmallGroup(92,4);
# by ID

G:=PCGroup([3,-2,-2,-23]);
// Polycyclic

G:=Group<a,b|a^2=b^46=1,a*b=b*a>;
// generators/relations

Export

Subgroup lattice of C2×C46 in TeX

׿
×
𝔽