Finite Group Databasebeta

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C3×#13048339 #72259743

order3888
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C23

Aliases

direct productC3×#13048339

Splittings

SylowC32×H(3,𝔽3) ⋊ C2×D4

Subgroups

subgroupG/H
center, hypercenterC2×C3D3×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC2×C3×H(3,𝔽3)C23×C3
FrattiniC2×C3C3×D33
FittingC2×C32×H(3,𝔽3)C23
socleC2×C33C2×D32
hypocenterC3×H(3,𝔽3)C2×C3×D4
LCSG ▷ C2×C3×H(3,𝔽3) ▷ C3×H(3,𝔽3)
UCSC1 ◁ C2×C3

1538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#72259648

GAP

Past the SmallGroups library coverage — no SmallGroups id.