Finite Group Databasebeta

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Cayley diagram

C2×#6016 #87738

order400
isoclinismisoclinic class of #1035
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C2

Aliases

direct productC2×#6016

Splittings

derived, SylowC25 ⋊ C2×C8

Subgroups

subgroupG/H
center, hypercenterC22#1035
commutator, hypocenterC25C2×C8
FrattiniC2×C5C2×AGL(1,𝔽5)
FittingC22×C25C4
socle, prime radicalC22×C5AGL(1,𝔽5)
cosocleDic25C22
LCSG ▷ C25
UCSC1 ◁ C22

33 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 400

A minimal faithful permutation representation — 2 generators on 35 points:

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

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#6016, C4⋊#6016, #11716417, …
maximal normal subgroup ofC4×#6016, C4⋊#6016, #11716417, …
maximal quotient ofC2×#87709, #11716414, C4×#6016, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 32);