Finite Group Databasebeta

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D3×#11864777 #72220397

order6912
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productD3×#11864777

Splittings

FittingC33×#127 ⋊ C23
SylowC33 ⋊ C22×#453

Subgroups

subgroupG/H
centerC2D3×#10595278
commutator, cosocleC2×C33×C4C25
FrattiniC2×C4C22×D33
FittingC33×#127C23
socleC2×C33C22×#120
hypercenter#127D33
hypocenterC33C22×#453
LCSG ▷ C2×C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

At least 7606 conjugacy classes of subgroups; only the 998 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

holomorph ofC3×Dic6, C3×D12

GAP

Past the SmallGroups library coverage — no SmallGroups id.