Finite Group Databasebeta

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D32×C25×C31 #42124439

order27900
automorphism?
homologyAbelianization (H1) = C22×C25×C31 · Schur multiplier (H2) = C2

Aliases

direct productD32×C25×C31
unambiguous semidirect product(C3×D3)⋊(C2×C25×C31)
unambiguous semidirect product(C3⋊D3)⋊(C2×C25×C31)

Splittings

Fitting, HallC32×C25×C31 ⋊ C22
derived, SylowC32 ⋊ C22×C25×C31
HallC32×C31 ⋊ C22×C25
HallC32×C25 ⋊ C22×C31

Subgroups

subgroupG/H
center, hypercenterC25×C31D32
commutator, hypocenterC32C22×C25×C31
FrattiniC5C5×D32×C31
FittingC32×C25×C31C22
socleC32×C5×C31C22×C5
prime radicalC5×D32×C31C5
cosocleC32×C5C22×C5×C31
LCSG ▷ C32
UCSC1 ◁ C25×C31

132 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6975 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 186);