Finite Group Databasebeta

← Prev (#44569087) Next (#44569089) →

C2×C3×C29×D31⋊C3 #44569088

order32364
automorphism?
homologyAbelianization (H1) = C22×C32×C29 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C29×D31⋊C3
unambiguous semidirect productD31⋊(C2×C32×C29)
unambiguous semidirect product(C31⋊C3)⋊(C22×C3×C29)
unambiguous semidirect product(C2×D31)⋊(C32×C29)
unambiguous semidirect product(C2×C31⋊C3)⋊(C2×C3×C29)
unambiguous semidirect product(C2×C3×D31)⋊(C3×C29)
unambiguous semidirect product(C2×C29×D31)⋊C32
unambiguous semidirect product(C2×C3×C29×D31)⋊C3

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C3×C29D31⋊C3
commutator, cosocle, hypocenterC31C22×C32×C29
FrattiniC1G
Fitting, socleC2×C3×C29×C31C2×C3
LCSG ▷ C31
UCSC1 ◁ C2×C3×C29

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5394

Conjugacy classes & character table

1914 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32364, 74);