Finite Group Databasebeta

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C32×#64330 #72220352

order2592
automorphism?
homologyAbelianization (H1) = C24×C32 · Schur multiplier (H2) = C25×C3

Aliases

direct productC32×#64330

Splittings

FittingC23×C34 ⋊ C22
SylowC34 ⋊ H(5,𝔽2)

Subgroups

subgroupG/H
centerC2×C32C22×D32
commutator, cosocleC2×C32C24×C32
FrattiniC2C22×C32×D32
FittingC23×C34C22
socleC2×C34C24
hypercenterC23×C32D32
hypocenterC32C32×H(5,𝔽2)
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C32 ◁ C23×C32

3466 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.