Finite Group Databasebeta

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D3×#374114 #72249295

order3072
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C212

Aliases

direct productD3×#374114

Splittings

FittingC3×#374114 ⋊ C2
SylowC3 ⋊ C2×#374114

Subgroups

subgroupG/H
centerC22C2×D3×#386
commutatorC22×C3×C4C24×C4
FrattiniC23×C4C24×D3
FittingC3×#374114C2
socleC22×C3C22×#386
prime radicalC2×D3×#3003C2
cosocleC23×C3×C4C25
hypercenter#374114D3
hypocenterC3C2×#374114
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24×C4 ◁ #374114

55214 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.