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C11×#237 #10587271

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

Aliases

direct productC11×#237

Splittings

FittingC3×D4×C11 ⋊ C2
HallC3×C11 ⋊ #41
SylowC3 ⋊ C11×#41

Subgroups

subgroupG/H
centerC2×C11C22×D3
commutator, cosocleC2×C3C23×C11
FrattiniC2C22×D3×C11
FittingC3×D4×C11C2
socleC2×C3×C11C23
hypercenterD4×C11D3
hypocenterC3C11×#41
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C11 ◁ D4×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)(16,20)(17,21);(15,17,18,21)(16,19,20,22);(13,14)(15,16)(17,19)(18,20)(21,22)

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11760930, #11760936, #11760943, …
maximal normal subgroup of#11760930, #11760936, #11760943, …
maximal quotient ofC11×#877, C11×#878, C11×#885, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 141);