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C32×AGL(1,𝔽5)×ΓL(1,𝔽32) #42124705

order27900
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×AGL(1,𝔽5)×ΓL(1,𝔽32)
unambiguous semidirect product(C32×AGL(1,𝔽5)×C31)⋊C5

Splittings

Fitting, socleC32×C5×C31 ⋊ C4×C5
derivedC5×C31 ⋊ C32×C4×C5
HallC32×C5×ΓL(1,𝔽32) ⋊ C4
HallC5×ΓL(1,𝔽32) ⋊ C32×C4
HallC32×C31 ⋊ C5×AGL(1,𝔽5)
SylowC31 ⋊ C32×C5×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC32AGL(1,𝔽5)×ΓL(1,𝔽32)
commutator, hypocenterC5×C31C32×C4×C5
FrattiniC1G
Fitting, socleC32×C5×C31C4×C5
prime radicalC32×D5×ΓL(1,𝔽32)C2
cosocleD5×C31C2×C32×C5
LCSG ▷ C5×C31
UCSC1 ◁ C32

156 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

495 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 452);