Finite Group Databasebeta

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D3×#61451 #72219827

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

Aliases

direct productD3×#61451

Splittings

FittingC3×#61451 ⋊ C2
SylowC3 ⋊ C2×#61451

Subgroups

subgroupG/H
centerC22C23×D3×D4
commutator, cosocleC2×C3×C4C26
FrattiniC2×C4C25×D3
FittingC3×#61451C2
socleC22×C3C24×D4
hypercenter#61451D3
hypocenterC3C2×#61451
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×#41 ◁ #61451

At least 8028 conjugacy classes of subgroups; only the 3701 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#10576928
maximal normal subgroup ofD3×#10576928
maximal quotient ofD3×#6453969
automorphism group of#4495, #4496, #4516, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.