Finite Group Databasebeta

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D3×#111516 #72270109

order3072
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C211

Aliases

direct productD3×#111516

Splittings

FittingC3×#111516 ⋊ C2
SylowC3 ⋊ C2×#111516

Subgroups

subgroupG/H
centerC23D3×#379
commutatorC25×C3C23×C4
FrattiniC26C23×D3
FittingC3×#111516C2
socleC23×C3C2×#379
prime radicalC22×D3×#392C2
cosocleC26×C3C24
hypercenter#111516D3
hypocenterC3C2×#111516
LCSG ▷ C25×C3 ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C26 ◁ #111516

78946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72219165
maximal normal subgroup ofD3×#72219165
maximal quotient ofD3×#72219159

GAP

Past the SmallGroups library coverage — no SmallGroups id.