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C2×C9×PSU(3,𝔽2) #13049261

order1296
isoclinismisoclinic class of PSU(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C23×C9 · Schur multiplier (H2) = C22×C3

Aliases

direct productC2×C9×PSU(3,𝔽2)

Splittings

FittingC2×C32×C9 ⋊ Q8
SylowC32×C9 ⋊ C2×Q8

Subgroups

subgroupG/H
center, hypercenterC2×C9PSU(3,𝔽2)
commutatorC3⋊D3C23×C9
FrattiniC3C2×C3×PSU(3,𝔽2)
FittingC2×C32×C9Q8
socleC2×C33C3×Q8
prime radicalC2×C3×C3⋊D3C22×C3
cosocleC3×C3⋊D3C23×C3
hypocenterC32C2×Q8×C9
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C2×C9

137 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2979);