Finite Group Databasebeta

C2×#11661865 #72258849

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

Aliases

direct productC2×#11661865

Splittings

FittingC2×C3×#3021 ⋊ C2
SylowC3 ⋊ C2×#60388

Subgroups

subgroupG/H
centerC22C2×D3×#120
commutator, cosocleC2×C3×C4C26
FrattiniC2×C4C25×D3
FittingC2×C3×#3021C2
socleC22×C3C22×#120
hypercenterC2×#3021D3
hypocenterC3C2×#60388
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#3021

44936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.