Finite Group Databasebeta

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D3×#14345 #72254580

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

Aliases

direct productD3×#14345

Splittings

FittingC3×#14345 ⋊ C2
SylowC3 ⋊ C2×#14345

Subgroups

subgroupG/H
center, FrattiniC24C24×D3
commutatorC23×C3C24×C4
FittingC3×#14345C2
socle, cosocleC24×C3C25
prime radicalC23×D3×D4C22
hypercenter#14345D3
hypocenterC3C2×#14345
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #14345

15348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

192 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.