Finite Group Databasebeta

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D3×#359639 #72249282

order3072
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C213

Aliases

direct productD3×#359639

Splittings

FittingC3×#359639 ⋊ C2
SylowC3 ⋊ C2×#359639

Subgroups

subgroupG/H
centerC22C2×D3×#379
commutatorC22×C3×C4C24×C4
FrattiniC23×C4C24×D3
FittingC3×#359639C2
socleC22×C3C22×#379
prime radicalC2×D3×#3484C2
cosocleC23×C3×C4C25
hypercenter#359639D3
hypocenterC3C2×#359639
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24×C4 ◁ #359639

88722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72214076
maximal normal subgroup ofD3×#72214076

GAP

Past the SmallGroups library coverage — no SmallGroups id.