Finite Group Databasebeta

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C22×C5×C9×ΓL(1,𝔽32) #42124535

order27900
isoclinismisoclinic class of ΓL(1,𝔽32)
automorphism?
homologyAbelianization (H1) = C22×C52×C9 · Schur multiplier (H2) = C2×C5

Aliases

direct productC22×C5×C9×ΓL(1,𝔽32)
unambiguous semidirect product(C22×C9×C31)⋊C52
unambiguous semidirect product(C22×C5×C9×C31)⋊C5

Splittings

FittingC22×C5×C9×C31 ⋊ C5
derived, SylowC31 ⋊ C22×C52×C9
HallC22×C9×C31 ⋊ C52
HallC9×C31 ⋊ C22×C52
HallC22×C31 ⋊ C52×C9

Subgroups

subgroupG/H
center, hypercenterC22×C5×C9ΓL(1,𝔽32)
commutator, hypocenterC31C22×C52×C9
FrattiniC3C22×C3×C5×ΓL(1,𝔽32)
FittingC22×C5×C9×C31C5
socleC22×C3×C5×C31C3×C5
prime radicalC22×C3×C5×ΓL(1,𝔽32)C3
cosocleC3×C31C22×C3×C52
LCSG ▷ C31
UCSC1 ◁ C22×C5×C9

240 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, 282);