Finite Group Databasebeta

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C4×C29×C31⋊C9 #44569016

order32364
automorphism?
homologyAbelianization (H1) = C4×C9×C29 · Schur multiplier (H2) = C1

Aliases

direct productC4×C29×C31⋊C9
unambiguous semidirect product(C4×C31)⋊(C9×C29)
unambiguous semidirect product(C4×C29×C31)⋊C9

Splittings

derived, SylowC31 ⋊ C4×C9×C29
HallC4×C29×C31 ⋊ C9
HallC29×C31 ⋊ C4×C9
HallC4×C31 ⋊ C9×C29

Subgroups

subgroupG/H
center, hypercenterC3×C4×C29C31⋊C3
commutator, hypocenterC31C4×C9×C29
FrattiniC2×C3C2×C29×C31⋊C3
FittingC3×C4×C29×C31C3
socle, prime radicalC2×C3×C29×C31C2×C3
cosocleC2×C3×C31C2×C3×C29
LCSG ▷ C31
UCSC1 ◁ C3×C4×C29

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32364

Conjugacy classes & character table

4524 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32364, 2);