Finite Group Databasebeta

C2×#11661940 #72270888

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

Aliases

direct productC2×#11661940

Splittings

FittingC2×C3×#3027 ⋊ C2
SylowC3 ⋊ C2×#60399

Subgroups

subgroupG/H
centerC22C2×D3×#120
commutator, cosocleC23×C3C26
FrattiniC23C25×D3
FittingC2×C3×#3027C2
socleC22×C3C22×#120
hypercenterC2×#3027D3
hypocenterC3C2×#60399
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#3027

46784 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

174 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.