Finite Group Databasebeta

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D3×#10716 #72249283

order1536
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productD3×#10716

Splittings

FittingC3×#10716 ⋊ C2
SylowC3 ⋊ C2×#10716

Subgroups

subgroupG/H
centerC2×C4C2×C42×D3
commutatorC2×C3×C4C22×C42
FrattiniC23×C4C23×D3
FittingC3×#10716C2
socleC22×C3C22×#95
prime radicalC25×D3D4
cosocleC23×C3×C4C24
hypercenter#10716D3
hypocenterC3C2×#10716
LCSG ▷ C2×C3×C4 ▷ C3
UCSC1 ◁ C2×C4 ◁ #10716

9860 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#374114, D3×#364424, D3×#359509, …
maximal normal subgroup ofD3×#374114, D3×#364424, D3×#359509, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.