Finite Group Databasebeta

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C22×C4×(C3⋊D3)⋊A4 #72269126

order3456
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C27×C3

Aliases

direct productC22×C4×(C3⋊D3)⋊A4

Splittings

FittingC24×C32×C4 ⋊ C2×C3
derivedC22×C32 ⋊ C23×C3×C4

Subgroups

subgroupG/H
center, hypercenterC22×C4(C3⋊D3)⋊A4
commutator, hypocenterC22×C32C23×C3×C4
FrattiniC2×C3C23×D3×A4
FittingC24×C32×C4C2×C3
socleC25×C3C2×C3×D3
prime radicalC23×(C3⋊D3)⋊A4C2
cosocleC23×C32C24×C3
LCSG ▷ C22×C32
UCSC1 ◁ C22×C4

11840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#72213266
maximal normal subgroup ofC4×#72213266

GAP

Past the SmallGroups library coverage — no SmallGroups id.