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C3×C5×A4×ΓL(1,𝔽32) #42124739

order27900
automorphism?
homologyAbelianization (H1) = C32×C52 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC3×C5×A4×ΓL(1,𝔽32)
unambiguous semidirect productC22⋊(C32×C5×ΓL(1,𝔽32))
unambiguous semidirect product(C22×C3)⋊(C3×C5×ΓL(1,𝔽32))
unambiguous semidirect product(C22×C5)⋊(C32×ΓL(1,𝔽32))
unambiguous semidirect product(C22×C3×C5)⋊(C3×ΓL(1,𝔽32))
unambiguous semidirect product(C3×A4×C31)⋊C52
unambiguous semidirect product(C3×C5×A4×C31)⋊C5

Splittings

Fitting, socleC22×C3×C5×C31 ⋊ C3×C5
derived, HallC22×C31 ⋊ C32×C52
HallC22×C5×ΓL(1,𝔽32) ⋊ C32
HallC3×A4×C31 ⋊ C52
SylowC31 ⋊ C3×C52×A4
SylowC22 ⋊ C32×C5×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC3×C5A4×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC22×C31C32×C52
FrattiniC1G
Fitting, socleC22×C3×C5×C31C3×C5
LCSG ▷ C22×C31
UCSC1 ◁ C3×C5

224 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, 486);