Finite Group Databasebeta

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D3×#59126 #72254423

order1536
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C215

Aliases

direct productD3×#59126

Splittings

FittingC3×#59126 ⋊ C2
SylowC3 ⋊ C2×#59126

Subgroups

subgroupG/H
center, FrattiniC23C25×D3
commutator, socle, cosocleC23×C3C26
FittingC3×#59126C2
hypercenter#59126D3
hypocenterC3C2×#59126
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #59126

40772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#7837029, D3×#7684106
maximal normal subgroup ofD3×#7837029, D3×#7684106
maximal quotient ofD3×#772778, D3×#772785

GAP

Past the SmallGroups library coverage — no SmallGroups id.