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C5×Dic9×ΓL(1,𝔽32) #42124348

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

Aliases

direct productC5×Dic9×ΓL(1,𝔽32)
unambiguous semidirect productC9⋊(C4×C5×ΓL(1,𝔽32))
unambiguous semidirect product(C31×Dic9)⋊C52
unambiguous semidirect product(C5×C31×Dic9)⋊C5

Splittings

derived, HallC9×C31 ⋊ C4×C52
HallC5×C9×ΓL(1,𝔽32) ⋊ C4
HallC31×Dic9 ⋊ C52
SylowC31 ⋊ C52×Dic9
SylowC9 ⋊ C4×C5×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC2×C5D9×ΓL(1,𝔽32)
commutator, hypocenterC9×C31C4×C52
FrattiniC2×C3C5×D3×ΓL(1,𝔽32)
FittingC2×C5×C9×C31C2×C5
socleC2×C3×C5×C31C5×D3
prime radicalC2×C3×C5×ΓL(1,𝔽32)D3
cosocleC2×C9×C31C2×C52
LCSG ▷ C9×C31
UCSC1 ◁ C2×C5

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 95);