Finite Group Databasebeta

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#67×C3⋊((C3⋊D3)⋊C3) #72260039

order3888
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C32

Aliases

direct product#67×C3⋊((C3⋊D3)⋊C3)

Splittings

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

Subgroups

subgroupG/H
centerC2C2×D3×C3⋊((C3⋊D3)⋊C3)
commutator, cosocleC2×C34C23×C3
FrattiniC2×C3C2×C3×D3×C3⋊D3
FittingC22×C32×H(3,𝔽3)C22
socleC2×C33C22×C3×D3
hypercenterC22D3×C3⋊((C3⋊D3)⋊C3)
hypocenterC34C2×C3×D4
LCSG ▷ C2×C34 ▷ C34
UCSC1 ◁ C2 ◁ C22

2482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.