Finite Group Databasebeta

← Prev (#37524558) Next (#37524560) →

C72×C9×#261 #37524559

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

Aliases

direct productC72×C9×#261

Splittings

Fitting, HallC72×C9×C13 ⋊ C4
derived, SylowC13 ⋊ C4×C72×C9
HallC72×C13 ⋊ C4×C9
HallC9×C13 ⋊ C4×C72

Subgroups

subgroupG/H
center, hypercenterC72×C9#261
commutator, hypocenterC13C4×C72×C9
FrattiniC3C3×C72×#261
FittingC72×C9×C13C4
socleC3×C72×C13C3×C4
prime radicalC3×C72×D13C2×C3
cosocleC3×D13C2×C3×C72
LCSG ▷ C13
UCSC1 ◁ C72×C9

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5733

Conjugacy classes & character table

3087 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 504);