Finite Group Databasebeta

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D3×#139743 #72231823

order3072
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productD3×#139743

Splittings

FittingC3×#139743 ⋊ C2
SylowC3 ⋊ C2×#139743

Subgroups

subgroupG/H
centerC2D3×#9495
commutatorC22×C3×D4C23×C4
FrattiniC23×D4C23×D3
FittingC3×#139743C2
socleC2×C3C2×#9495
prime radicalD3×#23895C2
cosocleC23×C3×D4C24
hypercenter#139743D3
hypocenterC3C2×#139743
LCSG ▷ C22×C3×D4 ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C23 ◁ C23×D4 ◁ #139743

10726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

123 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×B(5,𝔽2)
maximal normal subgroup ofD3×B(5,𝔽2)
maximal quotient ofD3×#72219160

GAP

Past the SmallGroups library coverage — no SmallGroups id.