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C32×C4×C5×ΓL(1,𝔽32) #42124648

order27900
isoclinismisoclinic class of ΓL(1,𝔽32)
automorphism?
homologyAbelianization (H1) = C32×C4×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC32×C4×C5×ΓL(1,𝔽32)
unambiguous semidirect product(C32×C4×C31)⋊C52
unambiguous semidirect product(C32×C4×C5×C31)⋊C5

Splittings

FittingC32×C4×C5×C31 ⋊ C5
derived, SylowC31 ⋊ C32×C4×C52
HallC32×C4×C31 ⋊ C52
HallC32×C31 ⋊ C4×C52
HallC4×C31 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC32×C4×C5ΓL(1,𝔽32)
commutator, hypocenterC31C32×C4×C52
FrattiniC2C2×C32×C5×ΓL(1,𝔽32)
FittingC32×C4×C5×C31C5
socleC2×C32×C5×C31C2×C5
prime radicalC2×C32×C5×ΓL(1,𝔽32)C2
cosocleC2×C31C2×C32×C52
LCSG ▷ C31
UCSC1 ◁ C32×C4×C5

288 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 395);