Finite Group Databasebeta

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D3×#495725 #72247523

order3072
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD3×#495725

Splittings

FittingC3×#495725 ⋊ C2
SylowC3 ⋊ C2×#495725

Subgroups

subgroupG/H
centerC22C2×D3×#442
commutatorC2×C3×C8C24×C4
FrattiniC22×C8C24×D3
FittingC3×#495725C2
socleC22×C3C22×#442
prime radicalD3×#33517C2
cosocleC22×C3×C8C25
hypercenter#495725D3
hypocenterC3C2×#495725
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#97 ◁ #495725

18910 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

automorphism group of#4504, #4505

GAP

Past the SmallGroups library coverage — no SmallGroups id.