Finite Group Databasebeta

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C2×D3×#23897 #72248237

order3072
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C216

Aliases

direct productC2×D3×#23897

Splittings

FittingC2×C3×#23897 ⋊ C2
SylowC3 ⋊ C22×#23897

Subgroups

subgroupG/H
centerC22D3×#2403
commutator, cosocleC22×C3×C4C26
FrattiniC22×C4C25×D3
FittingC2×C3×#23897C2
socleC22×C3C2×#2403
hypercenterC2×#23897D3
hypocenterC3C22×#23897
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#23897

140770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72213329, C2×D3×#511790, D3×#72210511, …
maximal normal subgroup ofD3×#72213329, C2×D3×#511790, D3×#72210511, …
maximal quotient ofD3×#72210511

GAP

Past the SmallGroups library coverage — no SmallGroups id.