Finite Group Databasebeta

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Cayley diagram

C2×#6599 #90799

order464
isoclinismisoclinic class of #1181
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C2

Aliases

direct productC2×#6599

Splittings

derived, SylowC29 ⋊ C2×C8

Subgroups

subgroupG/H
center, hypercenterC22#1181
commutator, hypocenterC29C2×C8
FrattiniC2C2×#1181
Fitting, socle, prime radicalC22×C29C4
cosocleDic29C22
LCSG ▷ C29
UCSC1 ◁ C22

22 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 464

A minimal faithful permutation representation — 2 generators on 39 points:

(3,4,5,7,6,8,9,10)(12,13,14,16)(15,18,19,25)(17,22,23,21)(20,27,28,35)(24,31,32,33)(26,34,29,30)(36,38,39,37);(1,2)(11,12,15,20,29,25,33,27,36,38,34,22,13,17,24,32,23,16,21,30,37,39,35,31,18,26,28,19,14)

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#6599, C4⋊#6599, #11745218, …
maximal normal subgroup ofC4×#6599, C4⋊#6599, #11745218, …
maximal quotient ofC2×#90770, #11745214, C4×#6599, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 32);