Finite Group Databasebeta

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C3×#11865254 #72220172

order3456
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C27

Aliases

direct productC3×#11865254

Splittings

FittingC33×#120 ⋊ C22
SylowC33 ⋊ C2×B(4,𝔽2)

Subgroups

subgroupG/H
centerC2×C3#10595278
commutator, cosocleC23×C32C24×C3
FrattiniC23C22×C3×D32
FittingC33×#120C22
socleC2×C33C2×#120
hypercenterC3×#120D32
hypocenterC32C2×C3×B(4,𝔽2)
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C3×#120

5260 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72220179, C3×#72210357, D3×#11865254
maximal normal subgroup ofD3×#11865254
maximal quotient of#72220179

GAP

Past the SmallGroups library coverage — no SmallGroups id.