Finite Group Databasebeta

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C32×#120×AGL(1,𝔽7) #72269489

order12096
automorphism?
homologyAbelianization (H1) = C24×C33 · Schur multiplier (H2) = C27×C33

Aliases

direct productC32×#120×AGL(1,𝔽7)

Splittings

FittingC32×C7×#120 ⋊ C2×C3
HallD7×#120 ⋊ C33
HallC32×ΓL(1,𝔽8) ⋊ C2×#120
SylowC7 ⋊ C2×C33×#120

Subgroups

subgroupG/H
centerC22×C32C23×AGL(1,𝔽7)
commutator, cosocleC22×C7C24×C33
FrattiniC22C23×C32×AGL(1,𝔽7)
FittingC32×C7×#120C2×C3
socleC22×C32×C7C24×C3
hypercenterC32×#120AGL(1,𝔽7)
hypocenterC7C2×C33×#120
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C32 ◁ C32×#120

18536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 504

Conjugacy classes & character table

882 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.