Finite Group Databasebeta

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D3×#11012 #72248205

order1536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productD3×#11012

Splittings

FittingC3×#11012 ⋊ C2
SylowC3 ⋊ C2×#11012

Subgroups

subgroupG/H
centerC22D3×#386
commutatorC22×C3×C4C23×C4
FrattiniC23×C4C23×D3
FittingC3×#11012C2
socleC22×C3C2×#386
prime radicalC22×D3×AGL(1,ℤ/8)C2
cosocleC23×C3×C4C24
hypercenter#11012D3
hypocenterC3C2×#11012
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #11012

9948 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#417597, D3×#417670, D3×#417774, …
maximal normal subgroup ofD3×#417597, D3×#417670, D3×#417774, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.