Finite Group Databasebeta

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#67×(C3⋊S4)⋊C3 #72222964

order5184
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C24×C3

Aliases

direct product#67×(C3⋊S4)⋊C3

Splittings

FittingC24×C33 ⋊ C2×D3

Subgroups

subgroupG/H
centerC2C2×D3×(C3⋊S4)⋊C3
commutator, cosocleC2×C32×A4C23×C3
FrattiniC2×C3C2×C3×D3×S4
FittingC24×C33C2×D3
socleC23×C32C22×C3×D3
hypercenterC22D3×(C3⋊S4)⋊C3
hypocenterC32×A4C2×C3×D4
LCSG ▷ C2×C32×A4 ▷ C32×A4
UCSC1 ◁ C2 ◁ C22

2360 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

171 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72222968
maximal normal subgroup of#72222993

GAP

Past the SmallGroups library coverage — no SmallGroups id.