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C72×C22⋊(C13⋊C9) #37524602

order22932
automorphism?
homologyAbelianization (H1) = C72×C9 · Schur multiplier (H2) = C2×C7

Aliases

direct productC72×C22⋊(C13⋊C9)
unambiguous semidirect productC22⋊(C72×C13⋊C9)
unambiguous semidirect productC13⋊(C72×C22⋊C9)

Splittings

derived, HallC22×C13 ⋊ C72×C9
HallC22×C72×C13 ⋊ C9
HallC72×C13 ⋊ C22⋊C9
HallC22×C72 ⋊ C13⋊C9
SylowC13 ⋊ C72×C22⋊C9
SylowC22 ⋊ C72×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C72C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C72×C9
FrattiniC3C72×C22⋊(C13⋊C3)
Fitting, socle, prime radicalC22×C3×C72×C13C3
cosocleC22×C3×C13C3×C72
LCSG ▷ C22×C13
UCSC1 ◁ C3×C72

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11466

Conjugacy classes & character table

2940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 547);