Finite Group Databasebeta

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C2×C29⋊(D31⋊C9) #44569032

order32364
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C29⋊(D31⋊C9)
unambiguous semidirect product(C2×C29)⋊(D31⋊C9)
unambiguous semidirect product(C2×C31⋊C9)⋊D29
unambiguous semidirect product(C2×D899)⋊C9

Splittings

derived, HallC29×C31 ⋊ C22×C9
HallC29×C31⋊C9 ⋊ C22
HallC2×D899 ⋊ C9
HallC31⋊C9 ⋊ C2×D29
SylowC31 ⋊ C2×C9×D29
SylowC29 ⋊ C2×D31⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3C29⋊(D31⋊C3)
commutator, hypocenterC29×C31C22×C9
FrattiniC3C2×C29⋊(D31⋊C3)
Fitting, socleC2×C3×C29×C31C2×C3
prime radicalC2×C3×D899C3
cosocleC3×C29×C31C22×C3
LCSG ▷ C29×C31
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16182

Conjugacy classes & character table

1158 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32364, 18);