Finite Group Databasebeta

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C3×C29×C22⋊(C31⋊C3) #44569131

order32364
automorphism?
homologyAbelianization (H1) = C32×C29 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C29×C22⋊(C31⋊C3)
unambiguous semidirect product(C22×C3)⋊(C29×C31⋊C3)
unambiguous semidirect product(C3×C31)⋊(A4×C29)
unambiguous semidirect product(C22×C3×C29)⋊(C31⋊C3)
unambiguous semidirect product(C3×C29×C31)⋊A4

Splittings

Fitting, socleC22×C3×C29×C31 ⋊ C3
derived, HallC22×C31 ⋊ C32×C29
HallC22×C29×C31 ⋊ C32
HallC29×C31 ⋊ C3×A4
HallC22×C29 ⋊ C3×C31⋊C3
SylowC31 ⋊ C3×A4×C29
SylowC22 ⋊ C3×C29×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C29C22⋊(C31⋊C3)
commutator, cosocle, hypocenterC22×C31C32×C29
FrattiniC1G
Fitting, socleC22×C3×C29×C31C3
LCSG ▷ C22×C31
UCSC1 ◁ C3×C29

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10788

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, 117);