Finite Group Databasebeta

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#135×PSU(3,𝔽2) #72245334

order2304
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28×C3

Aliases

direct product#135×PSU(3,𝔽2)

Splittings

FittingC32×#135 ⋊ Q8
SylowC32 ⋊ Q8×#135

Subgroups

subgroupG/H
centerC4D4×PSU(3,𝔽2)
commutator, cosocleC4×C3⋊D3C25
FrattiniC4C23×PSU(3,𝔽2)
FittingC32×#135Q8
socleC2×C32C2×D4×Q8
prime radicalC3⋊D3×#135C22
hypercenter#135PSU(3,𝔽2)
hypocenterC32Q8×#135
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

1919 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#135×PSU(3,𝔽2)⋊C3
maximal normal subgroup of#135×PSU(3,𝔽2)⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.