Finite Group Databasebeta

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M32×PSU(3,𝔽2) #72245133

order2304
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C3

Aliases

direct productM32×PSU(3,𝔽2)

Splittings

FittingC32×M32 ⋊ Q8
SylowC32 ⋊ Q8×M32

Subgroups

subgroupG/H
center, FrattiniC8C22×PSU(3,𝔽2)
commutatorC2×C3⋊D3C23×C8
FittingC32×M32Q8
socleC2×C32C2×C8×Q8
prime radicalC22×C3⋊D3C22×C8
cosocleC8×C3⋊D3C24
hypercenterM32PSU(3,𝔽2)
hypocenterC32Q8×M32
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C8 ◁ M32

575 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofM32×PSU(3,𝔽2)⋊C3
maximal normal subgroup ofM32×PSU(3,𝔽2)⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.