Finite Group Databasebeta

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D3×#499832 #72270595

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

Aliases

direct productD3×#499832

Splittings

FittingC3×#499832 ⋊ C2
SylowC3 ⋊ C2×#499832

Subgroups

subgroupG/H
centerC22C2×D3×B(4,𝔽2)
commutator, cosocleC22×C3×D4C25
FrattiniC22×D4C24×D3
FittingC3×#499832C2
socleC22×C3C22×B(4,𝔽2)
hypercenter#499832D3
hypocenterC3C2×#499832
LCSG ▷ C22×C3×D4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ #499832

At least 8140 conjugacy classes of subgroups; only the 915 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72210575
maximal normal subgroup ofD3×#72210575

GAP

Past the SmallGroups library coverage — no SmallGroups id.