Finite Group Databasebeta

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C2×C3×C29⋊(D31⋊C3) #44569089

order32364
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C29⋊(D31⋊C3)
unambiguous semidirect product(C2×C29)⋊(C3×D31⋊C3)
unambiguous semidirect product(C2×C31⋊C3)⋊(C3×D29)
unambiguous semidirect product(C2×D899)⋊C32
unambiguous semidirect product(C2×C3×D899)⋊C3

Splittings

Fitting, socleC2×C3×C29×C31 ⋊ C2×C3
derived, HallC29×C31 ⋊ C22×C32
HallC3×C29×C31⋊C3 ⋊ C22
HallC2×D899 ⋊ C32
HallC3×C31⋊C3 ⋊ C2×D29
SylowC31 ⋊ C2×C32×D29
SylowC29 ⋊ C2×C3×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3C29⋊(D31⋊C3)
commutator, cosocle, hypocenterC29×C31C22×C32
FrattiniC1G
Fitting, socleC2×C3×C29×C31C2×C3
LCSG ▷ C29×C31
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5394

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, 75);