Finite Group Databasebeta

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C2×D3×#73081 #72274936

order4608
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C28

Aliases

direct productC2×D3×#73081

Splittings

FittingC22×C3×#120 ⋊ C2×D3

Subgroups

subgroupG/H
center, hypercenterC22D3×#1020⋊C2
commutator, cosocleC2×C3×C22⋊A4C24
FrattiniC23C22×D3×S4
FittingC22×C3×#120C2×D3
socleC24×C3C22×S4
hypocenterC3×C22⋊A4C22×D4
LCSG ▷ C2×C3×C22⋊A4 ▷ C3×C22⋊A4
UCSC1 ◁ C22

21025 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×#11713200
maximal normal subgroup ofC2×D3×#11713200

GAP

Past the SmallGroups library coverage — no SmallGroups id.