Finite Group Databasebeta

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D3×#394102 #72249272

order3072
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C213

Aliases

direct productD3×#394102

Splittings

FittingC3×#394102 ⋊ C2
SylowC3 ⋊ C2×#394102

Subgroups

subgroupG/H
centerC22D3×#2403
commutator, cosocleC23×C3×C4C25
FrattiniC23×C4C24×D3
FittingC3×#394102C2
socleC22×C3C2×#2403
hypercenter#394102D3
hypocenterC3C2×#394102
LCSG ▷ C23×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #394102

91782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72214076
maximal normal subgroup ofD3×#72214076
automorphism group of#4552

GAP

Past the SmallGroups library coverage — no SmallGroups id.