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G = C2×C58order 116 = 22·29

Abelian group of type [2,58]

direct product, abelian, monomial, 2-elementary

Aliases: C2×C58, SmallGroup(116,5)

Series: Derived Chief Lower central Upper central

C1 — C2×C58
C1C29C58 — C2×C58
C1 — C2×C58
C1 — C2×C58

Generators and relations for C2×C58
 G = < a,b | a2=b58=1, ab=ba >


Smallest permutation representation of C2×C58
Regular action on 116 points
Generators in S116
(1 96)(2 97)(3 98)(4 99)(5 100)(6 101)(7 102)(8 103)(9 104)(10 105)(11 106)(12 107)(13 108)(14 109)(15 110)(16 111)(17 112)(18 113)(19 114)(20 115)(21 116)(22 59)(23 60)(24 61)(25 62)(26 63)(27 64)(28 65)(29 66)(30 67)(31 68)(32 69)(33 70)(34 71)(35 72)(36 73)(37 74)(38 75)(39 76)(40 77)(41 78)(42 79)(43 80)(44 81)(45 82)(46 83)(47 84)(48 85)(49 86)(50 87)(51 88)(52 89)(53 90)(54 91)(55 92)(56 93)(57 94)(58 95)
(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 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116)

G:=sub<Sym(116)| (1,96)(2,97)(3,98)(4,99)(5,100)(6,101)(7,102)(8,103)(9,104)(10,105)(11,106)(12,107)(13,108)(14,109)(15,110)(16,111)(17,112)(18,113)(19,114)(20,115)(21,116)(22,59)(23,60)(24,61)(25,62)(26,63)(27,64)(28,65)(29,66)(30,67)(31,68)(32,69)(33,70)(34,71)(35,72)(36,73)(37,74)(38,75)(39,76)(40,77)(41,78)(42,79)(43,80)(44,81)(45,82)(46,83)(47,84)(48,85)(49,86)(50,87)(51,88)(52,89)(53,90)(54,91)(55,92)(56,93)(57,94)(58,95), (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)(59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116)>;

G:=Group( (1,96)(2,97)(3,98)(4,99)(5,100)(6,101)(7,102)(8,103)(9,104)(10,105)(11,106)(12,107)(13,108)(14,109)(15,110)(16,111)(17,112)(18,113)(19,114)(20,115)(21,116)(22,59)(23,60)(24,61)(25,62)(26,63)(27,64)(28,65)(29,66)(30,67)(31,68)(32,69)(33,70)(34,71)(35,72)(36,73)(37,74)(38,75)(39,76)(40,77)(41,78)(42,79)(43,80)(44,81)(45,82)(46,83)(47,84)(48,85)(49,86)(50,87)(51,88)(52,89)(53,90)(54,91)(55,92)(56,93)(57,94)(58,95), (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)(59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116) );

G=PermutationGroup([(1,96),(2,97),(3,98),(4,99),(5,100),(6,101),(7,102),(8,103),(9,104),(10,105),(11,106),(12,107),(13,108),(14,109),(15,110),(16,111),(17,112),(18,113),(19,114),(20,115),(21,116),(22,59),(23,60),(24,61),(25,62),(26,63),(27,64),(28,65),(29,66),(30,67),(31,68),(32,69),(33,70),(34,71),(35,72),(36,73),(37,74),(38,75),(39,76),(40,77),(41,78),(42,79),(43,80),(44,81),(45,82),(46,83),(47,84),(48,85),(49,86),(50,87),(51,88),(52,89),(53,90),(54,91),(55,92),(56,93),(57,94),(58,95)], [(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),(59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116)])

C2×C58 is a maximal subgroup of   C29⋊D4

116 conjugacy classes

class 1 2A2B2C29A···29AB58A···58CF
order122229···2958···58
size11111···11···1

116 irreducible representations

dim1111
type++
imageC1C2C29C58
kernelC2×C58C58C22C2
# reps132884

Matrix representation of C2×C58 in GL2(𝔽59) generated by

580
01
,
260
024
G:=sub<GL(2,GF(59))| [58,0,0,1],[26,0,0,24] >;

C2×C58 in GAP, Magma, Sage, TeX

C_2\times C_{58}
% in TeX

G:=Group("C2xC58");
// GroupNames label

G:=SmallGroup(116,5);
// by ID

G=gap.SmallGroup(116,5);
# by ID

G:=PCGroup([3,-2,-2,-29]);
// Polycyclic

G:=Group<a,b|a^2=b^58=1,a*b=b*a>;
// generators/relations

Export

Subgroup lattice of C2×C58 in TeX

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