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G = C2×C44order 88 = 23·11

Abelian group of type [2,44]

direct product, abelian, monomial, 2-elementary

Aliases: C2×C44, SmallGroup(88,8)

Series: Derived Chief Lower central Upper central

C1 — C2×C44
C1C2C22C44 — C2×C44
C1 — C2×C44
C1 — C2×C44

Generators and relations for C2×C44
 G = < a,b | a2=b44=1, ab=ba >


Smallest permutation representation of C2×C44
Regular action on 88 points
Generators in S88
(1 74)(2 75)(3 76)(4 77)(5 78)(6 79)(7 80)(8 81)(9 82)(10 83)(11 84)(12 85)(13 86)(14 87)(15 88)(16 45)(17 46)(18 47)(19 48)(20 49)(21 50)(22 51)(23 52)(24 53)(25 54)(26 55)(27 56)(28 57)(29 58)(30 59)(31 60)(32 61)(33 62)(34 63)(35 64)(36 65)(37 66)(38 67)(39 68)(40 69)(41 70)(42 71)(43 72)(44 73)
(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)

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

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

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

C2×C44 is a maximal subgroup of   C44.C4  Dic11⋊C4  C44⋊C4  D22⋊C4  D445C2

88 conjugacy classes

class 1 2A2B2C4A4B4C4D11A···11J22A···22AD44A···44AN
order1222444411···1122···2244···44
size111111111···11···11···1

88 irreducible representations

dim11111111
type+++
imageC1C2C2C4C11C22C22C44
kernelC2×C44C44C2×C22C22C2×C4C4C22C2
# reps121410201040

Matrix representation of C2×C44 in GL2(𝔽89) generated by

10
088
,
680
067
G:=sub<GL(2,GF(89))| [1,0,0,88],[68,0,0,67] >;

C2×C44 in GAP, Magma, Sage, TeX

C_2\times C_{44}
% in TeX

G:=Group("C2xC44");
// GroupNames label

G:=SmallGroup(88,8);
// by ID

G=gap.SmallGroup(88,8);
# by ID

G:=PCGroup([4,-2,-2,-11,-2,176]);
// Polycyclic

G:=Group<a,b|a^2=b^44=1,a*b=b*a>;
// generators/relations

Export

Subgroup lattice of C2×C44 in TeX

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