Finite Group Databasebeta

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C2×C3⋊D3×#908 #72269013

order3456
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29×C3

Aliases

direct productC2×C3⋊D3×#908

Splittings

FittingC2×C33×M16 ⋊ C22
SylowC33 ⋊ C22×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C2×C3⋊D3×D12
commutator, cosocleC33×C4C25
FrattiniC4C23×D3×C3⋊D3
FittingC2×C33×M16C22
socleC22×C33C22×D4
hypercenterC2×M16D3×C3⋊D3
hypocenterC33C22×AGL(1,ℤ/8)
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

11512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.