Finite Group Databasebeta

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D3×C29×D31⋊C3 #44569079

order32364
automorphism?
homologyAbelianization (H1) = C22×C3×C29 · Schur multiplier (H2) = C2

Aliases

direct productD3×C29×D31⋊C3
unambiguous semidirect productD31⋊(C3×D3×C29)
unambiguous semidirect product(D3×D31)⋊(C3×C29)
unambiguous semidirect product(C3×D31⋊C3)⋊(C2×C29)
unambiguous semidirect product(D3×C31⋊C3)⋊(C2×C29)
unambiguous semidirect product(C3⋊(D31⋊C3))⋊(C2×C29)
unambiguous semidirect product(D3×C29×D31)⋊C3

Splittings

Fitting, socleC3×C29×C31 ⋊ C22×C3
derivedC3×C31 ⋊ C22×C3×C29
HallC3×C29×C31⋊C3 ⋊ C22
HallC29×C31 ⋊ C2×C3×D3
HallC3×C31⋊C3 ⋊ C22×C29
SylowC31 ⋊ C2×C3×D3×C29

Subgroups

subgroupG/H
center, hypercenterC29D3×D31⋊C3
commutator, cosocle, hypocenterC3×C31C22×C3×C29
FrattiniC1G
Fitting, socleC3×C29×C31C22×C3
LCSG ▷ C3×C31
UCSC1 ◁ C29

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2697

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32364, 65);