Finite Group Databasebeta

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D3×#60064 #72270354

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

Aliases

direct productD3×#60064

Splittings

FittingC3×#60064 ⋊ C2
SylowC3 ⋊ C2×#60064

Subgroups

subgroupG/H
center, FrattiniC2×C4C25×D3
commutator, socleC22×C3C25×C4
FittingC3×#60064C2
prime radicalC23×D3×#41C2
cosocleC2×C3×C4C26
hypercenter#60064D3
hypocenterC3C2×#60064
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ #60064

47540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×#359513, D3×#6437793, D3×#106740, …
maximal normal subgroup ofD3×#359513, D3×#6437793, D3×#106740, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.