Finite Group Databasebeta

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C22×C5×C11×#3862 #44568931

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2×C7

Aliases

direct productC22×C5×C11×#3862

Splittings

Fitting, socle, HallC22×C5×C72×C11 ⋊ C3
derived, SylowC72 ⋊ C22×C3×C5×C11
HallC5×C72×C11 ⋊ C22×C3
HallC22×C72×C11 ⋊ C3×C5
HallC22×C5×C72 ⋊ C3×C11
HallC72×C11 ⋊ C22×C3×C5
HallC5×C72 ⋊ C22×C3×C11
HallC22×C72 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC22×C5×C11#3862
commutator, cosocle, hypocenterC72C22×C3×C5×C11
FrattiniC1G
Fitting, socleC22×C5×C72×C11C3
LCSG ▷ C72
UCSC1 ◁ C22×C5×C11

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

4180 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 633);