Finite Group Databasebeta

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D3×#14357 #72248167

order1536
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211×C4

Aliases

direct productD3×#14357

Splittings

FittingC3×#14357 ⋊ C2
SylowC3 ⋊ C2×#14357

Subgroups

subgroupG/H
center, FrattiniC24C24×D3
commutatorC23×C3C24×C4
FittingC3×#14357C2
socle, cosocleC24×C3C25
prime radicalC22×D3×#120C2
hypercenter#14357D3
hypocenterC3C2×#14357
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #14357

30516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#846041, D3×#581603, D3×#1418391, …
maximal normal subgroup ofD3×#846041, D3×#581603, D3×#1418391, …
maximal quotient ofD3×#383145

GAP

Past the SmallGroups library coverage — no SmallGroups id.