Finite Group Databasebeta

C2×C3×C3⋊D3×#120 #72247145

order3456
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C211×C3

Aliases

direct productC2×C3×C3⋊D3×#120

Splittings

FittingC2×C33×#120 ⋊ C2
SylowC33 ⋊ C22×#120

Subgroups

subgroupG/H
centerC23×C3C23×C3⋊D3
commutator, cosocleC22×C32C25×C3
FrattiniC22C24×C3×C3⋊D3
FittingC2×C33×#120C2
socleC23×C33C24
hypercenterC2×C3×#120C3⋊D3
hypocenterC32C22×C3×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C2×C3×#120

29912 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.