Finite Group Databasebeta

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D3×#417674 #72253289

order3072
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C212

Aliases

direct productD3×#417674

Splittings

FittingC3×#417674 ⋊ C2
SylowC3 ⋊ C2×#417674

Subgroups

subgroupG/H
centerC22D3×#2668
commutator, cosocleC23×C3×C4C25
FrattiniC23×C4C24×D3
FittingC3×#417674C2
socleC22×C3C2×#2668
hypercenter#417674D3
hypocenterC3C2×#417674
LCSG ▷ C23×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #417674

At least 11790 conjugacy classes of subgroups; only the 1459 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72215520
maximal normal subgroup ofD3×#72215520

GAP

Past the SmallGroups library coverage — no SmallGroups id.