Finite Group Databasebeta

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C3×#66684⋊C3 #72246973

order3024
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3

Aliases

direct productC3×#66684⋊C3

Splittings

HallC32×ΓL(1,𝔽8) ⋊ #41
SylowC7 ⋊ C32×#237

Subgroups

subgroupG/H
centerC2×C3C2×D3×AGL(1,𝔽7)
commutator, cosocleC2×C3×C7C23×C32
FrattiniC2C2×C3×D3×AGL(1,𝔽7)
FittingC22×C32×C7C22×C3
socleC2×C32×C7C23×C3
hypercenterC22×C3D3×AGL(1,𝔽7)
hypocenterC3×C7C32×#41
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2×C3 ◁ C22×C3

608 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72246982, C3×AGL(1,𝔽7)×#237, #72247068, …
maximal normal subgroup of#72246982, C3×AGL(1,𝔽7)×#237, #72247068, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.