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C9×Dic5×ΓL(1,𝔽32) #42124346

order27900
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×Dic5×ΓL(1,𝔽32)
unambiguous semidirect product(C9×Dic5×C31)⋊C5

Splittings

derivedC5×C31 ⋊ C4×C5×C9
HallC5×C9×ΓL(1,𝔽32) ⋊ C4
HallC5×ΓL(1,𝔽32) ⋊ C4×C9
HallC9×C31 ⋊ C5×Dic5
SylowC31 ⋊ C5×C9×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C9D5×ΓL(1,𝔽32)
commutator, hypocenterC5×C31C4×C5×C9
FrattiniC2×C3C3×D5×ΓL(1,𝔽32)
FittingC2×C5×C9×C31C2×C5
socle, cosocleC2×C3×C5×C31C2×C3×C5
prime radicalC2×C3×C5×ΓL(1,𝔽32)C2×C3
LCSG ▷ C5×C31
UCSC1 ◁ C2×C9

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

792 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 93);