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C5×ΓL(1,𝔽32)⋊#157 #42124698

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

Aliases

direct productC5×ΓL(1,𝔽32)⋊#157
unambiguous semidirect productΓL(1,𝔽32)⋊(C5×#157)
unambiguous semidirect product(C31⋊#157)⋊C52
unambiguous semidirect product(C5×C31⋊#157)⋊C5

Splittings

Fitting, socleC32×C5×C31 ⋊ C4×C5
derived, HallC32×C31 ⋊ C4×C52
HallC32×C5×ΓL(1,𝔽32) ⋊ C4
HallC31⋊#157 ⋊ C52
HallC5×ΓL(1,𝔽32) ⋊ #157
SylowC31 ⋊ C52×#157
SylowC32 ⋊ C5×Dic31⋊C5

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽32)⋊#157
commutator, hypocenterC32×C31C4×C52
FrattiniC1G
Fitting, socleC32×C5×C31C4×C5
prime radicalC5×C3⋊D3×ΓL(1,𝔽32)C2
cosocleC3⋊D3×C31C2×C52
LCSG ▷ C32×C31
UCSC1 ◁ C5

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 445);