Finite Group Databasebeta

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D3×#394321 #72254128

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

Aliases

direct productD3×#394321

Splittings

FittingC3×#394321 ⋊ C2
SylowC3 ⋊ C2×#394321

Subgroups

subgroupG/H
centerC22C2×D3×#392
commutator, cosocleC23×C3×C4C25
FrattiniC23×C4C24×D3
FittingC3×#394321C2
socleC22×C3C22×#392
hypercenter#394321D3
hypocenterC3C2×#394321
LCSG ▷ C23×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24×C4 ◁ #394321

At least 10598 conjugacy classes of subgroups; only the 1775 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72214076
maximal normal subgroup ofD3×#72214076

GAP

Past the SmallGroups library coverage — no SmallGroups id.