Finite Group Databasebeta

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C2×#11661937 #72270910

order1536
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C215

Aliases

direct productC2×#11661937

Splittings

FittingC2×C3×#3484 ⋊ C2
SylowC3 ⋊ C2×#60399

Subgroups

subgroupG/H
centerC22C22×#937
commutator, cosocleC23×C3C26
FrattiniC23C25×D3
FittingC2×C3×#3484C2
socleC22×C3C22×#120
hypercenterC2×#3484D3
hypocenterC3C2×#60399
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×D4 ◁ C2×#3484

46784 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×#60399
maximal normal subgroup ofC2×D3×#60399

GAP

Past the SmallGroups library coverage — no SmallGroups id.