Finite Group Databasebeta

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D3×#14171 #72255142

order1536
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C212

Aliases

direct productD3×#14171

Splittings

FittingC3×#14171 ⋊ C2
SylowC3 ⋊ C2×#14171

Subgroups

subgroupG/H
center, FrattiniC24C24×D3
commutatorC23×C3C24×C4
FittingC3×#14171C2
socle, cosocleC24×C3C25
prime radicalC2×D3×#392C2
hypercenter#14171D3
hypocenterC3C2×#14171
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #14171

23460 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×#772778, D3×#1418391, D3×#1260433, …
maximal normal subgroup ofD3×#772778, D3×#1418391, D3×#1260433, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.