Finite Group Databasebeta

← Prev (#72269407) Next (#72269409) →

C3×#72245539 #72269408

order6048
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3

Aliases

direct productC3×#72245539

Splittings

HallC32×ΓL(1,𝔽8) ⋊ AGL(1,ℤ/8)
SylowC7 ⋊ C32×#932

Subgroups

subgroupG/H
centerC2×C3C2×#4245⋊C3
commutator, cosocleC3×C4×C7C23×C32
FrattiniC4C2×C3×D3×AGL(1,𝔽7)
FittingC2×C32×C4×C7C22×C3
socleC2×C32×C7C2×C3×D4
hypercenterC2×C3×C4D3×AGL(1,𝔽7)
hypocenterC3×C7C32×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2×C3 ◁ C2×C3×C4

1248 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

243 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72269413, C3×AGL(1,𝔽7)×#932
maximal normal subgroup of#72269413, C3×AGL(1,𝔽7)×#932

GAP

Past the SmallGroups library coverage — no SmallGroups id.