Finite Group Databasebeta

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C3×C4×C29×C31⋊C3 #44569063

order32364
automorphism?
homologyAbelianization (H1) = C32×C4×C29 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C29×C31⋊C3
unambiguous semidirect product(C4×C31)⋊(C32×C29)
unambiguous semidirect product(C3×C4×C31)⋊(C3×C29)
unambiguous semidirect product(C4×C29×C31)⋊C32
unambiguous semidirect product(C3×C4×C29×C31)⋊C3

Splittings

FittingC3×C4×C29×C31 ⋊ C3
derived, SylowC31 ⋊ C32×C4×C29
HallC4×C29×C31 ⋊ C32
HallC29×C31 ⋊ C32×C4
HallC4×C31 ⋊ C32×C29

Subgroups

subgroupG/H
center, hypercenterC3×C4×C29C31⋊C3
commutator, hypocenterC31C32×C4×C29
FrattiniC2C2×C3×C29×C31⋊C3
FittingC3×C4×C29×C31C3
socleC2×C3×C29×C31C2×C3
prime radicalC2×C3×C29×C31⋊C3C2
cosocleC2×C31C2×C32×C29
LCSG ▷ C31
UCSC1 ◁ C3×C4×C29

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10788

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, 49);