Finite Group Databasebeta

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D3×#34256 #72253456

order1536
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C215

Aliases

direct productD3×#34256

Splittings

FittingC3×#34256 ⋊ C2
SylowC3 ⋊ C2×#34256

Subgroups

subgroupG/H
center, FrattiniC23C25×D3
commutatorC22×C3C25×C4
FittingC3×#34256C2
socle, cosocleC23×C3C26
prime radicalC22×D3×H(5,𝔽2)C2
hypercenter#34256D3
hypocenterC3C2×#34256
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #34256

53252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×#7631286
maximal normal subgroup ofD3×#7631286
maximal quotient ofD3×#581603, D3×#574938, D3×#518019, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.