Finite Group Databasebeta

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C9×C31×#1181 #44569034

order32364
automorphism?
homologyAbelianization (H1) = C4×C9×C31 · Schur multiplier (H2) = C1

Aliases

direct productC9×C31×#1181

Splittings

Fitting, HallC9×C29×C31 ⋊ C4
derived, SylowC29 ⋊ C4×C9×C31
HallC29×C31 ⋊ C4×C9
HallC9×C29 ⋊ C4×C31

Subgroups

subgroupG/H
center, hypercenterC9×C31#1181
commutator, hypocenterC29C4×C9×C31
FrattiniC3C3×C31×#1181
FittingC9×C29×C31C4
socleC3×C29×C31C3×C4
prime radicalC3×C31×D29C2×C3
cosocleC3×D29C2×C3×C31
LCSG ▷ C29
UCSC1 ◁ C9×C31

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8091

Conjugacy classes & character table

3069 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32364, 20);