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C3×D88 #10587164

order528
isoclinismisoclinic class of #4314
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D88

Splittings

FittingC3×C8×C11 ⋊ C2
HallC3×C11 ⋊ D8
SylowC11 ⋊ C3×D8

Subgroups

subgroupG/H
centerC2×C3D44
commutator, cosocleC4×C11C22×C3
FrattiniC4C2×C3×D11
FittingC3×C8×C11C2
socleC2×C3×C11D4
hypercenterC3×C8D11
hypocenterC11C3×D8
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 264

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2,3)(4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22);(5,11)(6,10)(7,9)(13,22)(14,21)(15,20)(16,19)(17,18)

Conjugacy classes & character table

141 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11760474, #11760475, #11760477, …
maximal normal subgroup of#11760474, #11760475, #11760477, …
maximal quotient ofC3×#66864, C3×D176, C3×Dic88, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 34);