Finite Group Databasebeta

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D3×#13959 #72254703

order1536
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210×C4

Aliases

direct productD3×#13959

Splittings

FittingC3×#13959 ⋊ C2
SylowC3 ⋊ C2×#13959

Subgroups

subgroupG/H
center, FrattiniC24C24×D3
commutatorC23×C3C24×C4
FittingC3×#13959C2
socle, cosocleC24×C3C25
prime radicalC23×D3×D4C22
hypercenter#13959D3
hypocenterC3C2×#13959
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #13959

15876 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#619101, D3×#574938, D3×#4929019, …
maximal normal subgroup ofD3×#619101, D3×#574938, D3×#4929019, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.