Finite Group Databasebeta

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D3×#11865254 #72258328

order6912
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productD3×#11865254

Splittings

FittingC33×#120 ⋊ C23
SylowC33 ⋊ C22×B(4,𝔽2)

Subgroups

subgroupG/H
centerC2D3×#10595278
commutator, cosocleC23×C33C25
FrattiniC23C22×D33
FittingC33×#120C23
socleC2×C33C22×#120
hypercenter#120D33
hypocenterC33C22×B(4,𝔽2)
LCSG ▷ C23×C33 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C23 ◁ #120

35298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72210357
holomorph ofC2×C3×Dic3

GAP

Past the SmallGroups library coverage — no SmallGroups id.