Finite Group Databasebeta

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C29×Dic31⋊C9 #44569024

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

Aliases

direct productC29×Dic31⋊C9
unambiguous semidirect productDic31⋊(C9×C29)
unambiguous semidirect product(C31⋊C9)⋊(C4×C29)
unambiguous semidirect product(C29×Dic31)⋊C9

Splittings

derived, SylowC31 ⋊ C4×C9×C29
HallC29×C31⋊C9 ⋊ C4
HallC29×Dic31 ⋊ C9
HallC29×C31 ⋊ C4×C9
HallC31⋊C9 ⋊ C4×C29
HallDic31 ⋊ C9×C29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C29D31⋊C3
commutator, hypocenterC31C4×C9×C29
FrattiniC2×C3C29×D31⋊C3
Fitting, socle, prime radicalC2×C3×C29×C31C2×C3
cosocleC2×C3×C31C2×C3×C29
LCSG ▷ C31
UCSC1 ◁ C2×C3×C29

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32364

Conjugacy classes & character table

1914 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32364, 10);