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C5×C3⋊Dic3×ΓL(1,𝔽32) #42124615

order27900
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC5×C3⋊Dic3×ΓL(1,𝔽32)
unambiguous semidirect productC3⋊(C5×Dic3×ΓL(1,𝔽32))
unambiguous semidirect product(C31×C3⋊Dic3)⋊C52
unambiguous semidirect product(C5×C31×C3⋊Dic3)⋊C5

Splittings

derived, HallC32×C31 ⋊ C4×C52
HallC32×C5×ΓL(1,𝔽32) ⋊ C4
HallC31×C3⋊Dic3 ⋊ C52
SylowC31 ⋊ C52×C3⋊Dic3
SylowC32 ⋊ C4×C5×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊D3×ΓL(1,𝔽32)
commutator, hypocenterC32×C31C4×C52
FrattiniC2C5×C3⋊D3×ΓL(1,𝔽32)
Fitting, socleC2×C32×C5×C31C2×C5
prime radicalC2×C32×C5×ΓL(1,𝔽32)C2
cosocleC2×C32×C31C2×C52
LCSG ▷ C32×C31
UCSC1 ◁ C2×C5

288 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, 362);