Finite Group Databasebeta

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C29×C22⋊(C31⋊C9) #44569045

order32364
automorphism?
homologyAbelianization (H1) = C9×C29 · Schur multiplier (H2) = C2

Aliases

direct productC29×C22⋊(C31⋊C9)
unambiguous semidirect productC22⋊(C29×C31⋊C9)
unambiguous semidirect productC31⋊(C29×C22⋊C9)
unambiguous semidirect product(C22×C29)⋊(C31⋊C9)
unambiguous semidirect product(C29×C31)⋊(C22⋊C9)

Splittings

derived, HallC22×C31 ⋊ C9×C29
HallC22×C29×C31 ⋊ C9
HallC29×C31 ⋊ C22⋊C9
HallC22×C29 ⋊ C31⋊C9
SylowC31 ⋊ C29×C22⋊C9
SylowC22 ⋊ C29×C31⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C29C22⋊(C31⋊C3)
commutator, hypocenterC22×C31C9×C29
FrattiniC3C29×C22⋊(C31⋊C3)
Fitting, socle, prime radicalC22×C3×C29×C31C3
cosocleC22×C3×C31C3×C29
LCSG ▷ C22×C31
UCSC1 ◁ C3×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16182

Conjugacy classes & character table

3828 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32364, 31);