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C4×C5×ΓL(1,𝔽32)⋊C9 #42124343

order27900
automorphism?
homologyAbelianization (H1) = C4×C52×C9 · Schur multiplier (H2) = C5

Aliases

direct productC4×C5×ΓL(1,𝔽32)⋊C9
unambiguous semidirect product(C4×ΓL(1,𝔽32))⋊(C5×C9)
unambiguous semidirect product(C4×C31⋊C9)⋊C52
unambiguous semidirect product(C4×C5×ΓL(1,𝔽32))⋊C9
unambiguous semidirect product(C4×C5×C31⋊C9)⋊C5

Splittings

derived, SylowC31 ⋊ C4×C52×C9
HallC4×C5×ΓL(1,𝔽32) ⋊ C9
HallC4×C31⋊C9 ⋊ C52
HallC5×ΓL(1,𝔽32) ⋊ C4×C9
HallC31⋊C9 ⋊ C4×C52
HallC4×C31 ⋊ C52×C9

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5(C31⋊C3)⋊C5
commutator, hypocenterC31C4×C52×C9
FrattiniC2×C3C2×C5×(C31⋊C3)⋊C5
FittingC3×C4×C5×C31C3×C5
socleC2×C3×C5×C31C2×C3×C5
prime radicalC2×C3×C5×ΓL(1,𝔽32)C2×C3
cosocleC2×C3×C31C2×C3×C52
LCSG ▷ C31
UCSC1 ◁ C3×C4×C5

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1020 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 90);