Finite Group Databasebeta

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C3×#89039⋊C3 #72259677

order3888
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C32

Aliases

direct productC3×#89039⋊C3

Splittings

FittingC22×C32×H(3,𝔽3) ⋊ C22
SylowC32×H(3,𝔽3) ⋊ C2×D4

Subgroups

subgroupG/H
centerC2×C3C2×D3×(C3⋊D3)⋊C3
commutator, cosocleC2×C33C23×C32
FrattiniC2×C3C2×C32×D32
FittingC22×C32×H(3,𝔽3)C22
socleC2×C33C22×C3×D3
hypercenterC22×C3D3×(C3⋊D3)⋊C3
hypocenterC33C2×C32×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C3 ◁ C22×C3

2144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Conjugacy classes & character table

243 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72259680
maximal quotient of#72259680

GAP

Past the SmallGroups library coverage — no SmallGroups id.