Finite Group Databasebeta

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D3×#23400 #72248641

order1536
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productD3×#23400

Splittings

FittingC3×#23400 ⋊ C2
SylowC3 ⋊ C2×#23400

Subgroups

subgroupG/H
centerC22C2×D3×#120
commutator, cosocleC22×C3×C4C25
FrattiniC22×C4C24×D3
FittingC3×#23400C2
socleC22×C3C22×#120
hypercenter#23400D3
hypocenterC3C2×#23400
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #23400

15940 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#417597, D3×#394102, D3×#6437475
maximal normal subgroup ofD3×#417597, D3×#394102, D3×#6437475

GAP

Past the SmallGroups library coverage — no SmallGroups id.