Finite Group Databasebeta

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D3×#61519 #72249265

order1536
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productD3×#61519

Splittings

FittingC3×#61519 ⋊ C2
SylowC3 ⋊ C2×#61519

Subgroups

subgroupG/H
centerC22C23×D3×D4
commutator, cosocleC2×C3×C4C26
FrattiniC2×C4C25×D3
FittingC3×#61519C2
socleC22×C3C24×D4
hypercenter#61519D3
hypocenterC3C2×#61519
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #529 ◁ #61519

14200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#10576928
maximal normal subgroup ofD3×#10576928

GAP

Past the SmallGroups library coverage — no SmallGroups id.