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C11×#239 #10587273

order528
automorphism?
homologyAbelianization (H1) = C23×C11 · Schur multiplier (H2) = C22

Aliases

direct productC11×#239

Splittings

FittingC3×Q8×C11 ⋊ C2
HallC3×C11 ⋊ #41
SylowC3 ⋊ C11×#41

Subgroups

subgroupG/H
centerC2×C11C22×D3
commutator, cosocleC2×C3C23×C11
FrattiniC2C22×D3×C11
FittingC3×Q8×C11C2
socleC2×C3×C11C23
hypercenterQ8×C11D3
hypocenterC3C11×#41
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C11 ◁ Q8×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 22 points:

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

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11760954, #11760960, #11760967, …
maximal normal subgroup of#11760954, #11760960, #11760967, …
maximal quotient ofC11×#890, C11×#892, C11×#893, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 143);