Finite Group Databasebeta

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C2×#13180597 #72269128

order3456
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13180597

Splittings

SylowC33 ⋊ C22×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×D3×GO+(4,𝔽2)
commutator, cosocleC3×C3⋊Dic3C25
FrattiniC2C22×D3×GO+(4,𝔽2)
FittingC23×C33C2×D4
socleC22×C33C22×D4
hypercenterC23D3×GO+(4,𝔽2)
hypocenterC33C22×AGL(1,ℤ/8)
LCSG ▷ C3×C3⋊Dic3 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

6676 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.