Finite Group Databasebeta

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C3⋊D3×#127×AGL(1,𝔽7) #72246609

order24192
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C29×C3×C4

Aliases

direct productC3⋊D3×#127×AGL(1,𝔽7)

Splittings

FittingC32×C7×#127 ⋊ C22×C3
HallC32×ΓL(1,𝔽8) ⋊ C22×#127
SylowC7 ⋊ C2×C3×C3⋊D3×#127

Subgroups

subgroupG/H
center, FrattiniC22C23×C3⋊D3×AGL(1,𝔽7)
commutator, socle, cosocleC22×C32×C7C25×C3
FittingC32×C7×#127C22×C3
hypercenter#127C3⋊D3×AGL(1,𝔽7)
hypocenterC32×C7C22×C3×#127
LCSG ▷ C22×C32×C7 ▷ C32×C7
UCSC1 ◁ C22 ◁ #127

39984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1008

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.