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D3×#120×AGL(1,𝔽7) #72244238

order8064
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C211

Aliases

direct productD3×#120×AGL(1,𝔽7)

Splittings

FittingC3×C7×#120 ⋊ C22×C3
HallC3×ΓL(1,𝔽8) ⋊ C22×#120
SylowC7 ⋊ C2×C3×D3×#120

Subgroups

subgroupG/H
center, FrattiniC22C23×D3×AGL(1,𝔽7)
commutator, socle, cosocleC22×C3×C7C25×C3
FittingC3×C7×#120C22×C3
hypercenter#120D3×AGL(1,𝔽7)
hypocenterC3×C7C22×C3×#120
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ #120

18838 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×AGL(1,𝔽7)×B(4,𝔽2)
maximal normal subgroup ofD3×AGL(1,𝔽7)×B(4,𝔽2)
maximal quotient ofD3×AGL(1,𝔽7)×#453, D3×AGL(1,𝔽7)×B(4,𝔽2)

GAP

Past the SmallGroups library coverage — no SmallGroups id.