Finite Group Databasebeta

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C4×C72×C13⋊C9 #37524379

order22932
automorphism?
homologyAbelianization (H1) = C4×C72×C9 · Schur multiplier (H2) = C7

Aliases

direct productC4×C72×C13⋊C9
unambiguous semidirect product(C4×C13)⋊(C72×C9)

Splittings

derived, SylowC13 ⋊ C4×C72×C9
HallC4×C72×C13 ⋊ C9
HallC72×C13 ⋊ C4×C9
HallC4×C13 ⋊ C72×C9

Subgroups

subgroupG/H
center, hypercenterC3×C4×C72C13⋊C3
commutator, hypocenterC13C4×C72×C9
FrattiniC2×C3C2×C72×C13⋊C3
FittingC3×C4×C72×C13C3
socle, prime radicalC2×C3×C72×C13C2×C3
cosocleC2×C3×C13C2×C3×C72
LCSG ▷ C13
UCSC1 ◁ C3×C4×C72

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22932

Conjugacy classes & character table

4116 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 324);