Finite Group Databasebeta

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C5×C72×C11×A4 #44568925

order32340
automorphism?
homologyAbelianization (H1) = C3×C5×C72×C11 · Schur multiplier (H2) = C2×C7

Aliases

direct productC5×C72×C11×A4
unambiguous semidirect productC22⋊(C3×C5×C72×C11)
unambiguous semidirect product(C22×C5)⋊(C3×C72×C11)
unambiguous semidirect product(C22×C5×C11)⋊(C3×C72)

Splittings

Fitting, socle, HallC22×C5×C72×C11 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C72×C11
HallC22×C72×C11 ⋊ C3×C5
HallC22×C5×C72 ⋊ C3×C11
HallC22×C5×C11 ⋊ C3×C72
HallC22×C72 ⋊ C3×C5×C11
HallC22×C11 ⋊ C3×C5×C72
HallC22×C5 ⋊ C3×C72×C11

Subgroups

subgroupG/H
center, hypercenterC5×C72×C11A4
commutator, cosocle, hypocenterC22C3×C5×C72×C11
FrattiniC1G
Fitting, socleC22×C5×C72×C11C3
LCSG ▷ C22
UCSC1 ◁ C5×C72×C11

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10780

Conjugacy classes & character table

10780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 627);