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C22×C9×C31⋊C25 #42124287

order27900
automorphism?
homologyAbelianization (H1) = C22×C9×C25 · Schur multiplier (H2) = C2

Aliases

direct productC22×C9×C31⋊C25
unambiguous semidirect product(C22×C9×C31)⋊C25

Splittings

derived, SylowC31 ⋊ C22×C9×C25
HallC22×C9×C31 ⋊ C25
HallC9×C31 ⋊ C22×C25
HallC22×C31 ⋊ C9×C25

Subgroups

subgroupG/H
center, hypercenterC22×C5×C9ΓL(1,𝔽32)
commutator, hypocenterC31C22×C9×C25
FrattiniC3×C5C22×C3×ΓL(1,𝔽32)
FittingC22×C5×C9×C31C5
socle, prime radicalC22×C3×C5×C31C3×C5
cosocleC3×C5×C31C22×C3×C5
LCSG ▷ C31
UCSC1 ◁ C22×C5×C9

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 34);