Finite Group Databasebeta

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#108×PSU(3,𝔽2) #72245214

order2304
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C3

Aliases

direct product#108×PSU(3,𝔽2)

Splittings

FittingC32×#108 ⋊ Q8
SylowC32 ⋊ Q8×#108

Subgroups

subgroupG/H
centerC4D4×PSU(3,𝔽2)
commutatorC4×C3⋊D3C23×C4
FrattiniC2×C4C22×PSU(3,𝔽2)
FittingC32×#108Q8
socleC2×C32Q8×C4⋊C4
prime radicalC22×C3⋊D3C22×Q8
cosocleC2×C4×C3⋊D3C24
hypercenter#108PSU(3,𝔽2)
hypocenterC32Q8×#108
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

711 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#108×PSU(3,𝔽2)⋊C3
maximal normal subgroup of#108×PSU(3,𝔽2)⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.