Finite Group Databasebeta

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D3×D4×#120 #72246456

order1536
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C216

Aliases

direct productD3×D4×#120

Splittings

FittingC3×D4×#120 ⋊ C2
SylowC3 ⋊ C2×D4×#120

Subgroups

subgroupG/H
center, FrattiniC23C25×D3
commutator, socle, cosocleC23×C3C26
FittingC3×D4×#120C2
hypercenterD4×#120D3
hypocenterC3C2×D4×#120
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ D4×#120

82404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#7849701, D3×#7792761, C2×D3×D4×#120, …
maximal normal subgroup ofD3×#7849701, D3×#7792761, C2×D3×D4×#120, …
maximal quotient ofD3×#846041, D3×#647656, C2×D3×D4×#120, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.