Finite Group Databasebeta

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D3×#106740 #72271406

order3072
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productD3×#106740

Splittings

FittingC3×#106740 ⋊ C2
SylowC3 ⋊ C2×#106740

Subgroups

subgroupG/H
centerC22D3×C22⋊#95
commutatorC22×C3×C4C22×C42
FrattiniC24×C4C23×D3
FittingC3×#106740C2
socleC22×C3C2×C22⋊#95
prime radicalC23×D3×#41C22
cosocleC24×C3×C4C24
hypercenter#106740D3
hypocenterC3C2×#106740
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24×C4 ◁ #106740

31466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

222 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72213396
maximal normal subgroup ofD3×#72213396

GAP

Past the SmallGroups library coverage — no SmallGroups id.