Finite Group Databasebeta

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C2×#13164733 #72252638

order3456
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC2×#13164733

Splittings

FittingC22×C3×D4×C9 ⋊ C22
SylowC3×C9 ⋊ C22×H(5,𝔽2)

Subgroups

subgroupG/H
centerC22C23×D3×D9
commutator, cosocleC2×C3×C9C26
FrattiniC2×C3C24×D32
FittingC22×C3×D4×C9C22
socleC22×C32C24×D3
hypercenterC22×D4D3×D9
hypocenterC3×C9C22×H(5,𝔽2)
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22×D4

21042 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

318 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.