Finite Group Databasebeta

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C22×C11⋊C5×#3861 #44568616

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

Aliases

direct productC22×C11⋊C5×#3861
unambiguous semidirect product(C22×C11×#3861)⋊C5

Splittings

Fitting, socle, HallC22×C72×C11 ⋊ C3×C5
derived, HallC72×C11 ⋊ C22×C3×C5
HallC22×C72×C11⋊C5 ⋊ C3
HallC22×C11×#3861 ⋊ C5
HallC72×C11⋊C5 ⋊ C22×C3
HallC11×#3861 ⋊ C22×C5
HallC22×C72 ⋊ C3×C11⋊C5
SylowC72 ⋊ C22×C3×C11⋊C5
HallC22×C11 ⋊ C5×#3861
SylowC11 ⋊ C22×C5×#3861

Subgroups

subgroupG/H
center, hypercenterC22C11⋊C5×#3861
commutator, cosocle, hypocenterC72×C11C22×C3×C5
FrattiniC1G
Fitting, socleC22×C72×C11C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C22

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2156

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 318);