Finite Group Databasebeta

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(C3⋊D3)⋊C3×#453 #72258392

order3456
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26×C3

Aliases

direct product(C3⋊D3)⋊C3×#453

Splittings

FittingH(3,𝔽3)×#453 ⋊ C2
SylowH(3,𝔽3) ⋊ C2×#453

Subgroups

subgroupG/H
centerC2#120×(C3⋊D3)⋊C3
commutator, cosocleC2×C32×C4C24×C3
FrattiniC2×C3×C4C23×C3×D3
FittingH(3,𝔽3)×#453C2
socleC2×C3C3×D3×#120
hypercenter#453(C3⋊D3)⋊C3
hypocenterC32C2×C3×#453
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

3122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.