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C29×C31×Dic9 #44569020

order32364
automorphism?
homologyAbelianization (H1) = C4×C29×C31 · Schur multiplier (H2) = C1

Aliases

direct productC29×C31×Dic9
unambiguous semidirect productC9⋊(C4×C29×C31)

Splittings

derived, SylowC9 ⋊ C4×C29×C31
HallC9×C29×C31 ⋊ C4
HallC9×C31 ⋊ C4×C29
HallC9×C29 ⋊ C4×C31

Subgroups

subgroupG/H
center, hypercenterC2×C29×C31D9
commutator, hypocenterC9C4×C29×C31
FrattiniC2×C3D3×C29×C31
FittingC2×C9×C29×C31C2
socle, prime radicalC2×C3×C29×C31D3
cosocleC2×C9C2×C29×C31
LCSG ▷ C9
UCSC1 ◁ C2×C29×C31

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32364

Conjugacy classes & character table

10788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32364, 6);