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AGL(1,𝔽7)×#1009 #72244456

order4032
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C29

Aliases

direct productAGL(1,𝔽7)×#1009

Splittings

FittingC3×C7×#41 ⋊ C22×C3
HallC3×ΓL(1,𝔽8) ⋊ C2×H(5,𝔽2)
SylowC7 ⋊ C2×C3×#1009

Subgroups

subgroupG/H
center, FrattiniC2C23×D3×AGL(1,𝔽7)
commutator, socle, cosocleC2×C3×C7C25×C3
FittingC3×C7×#41C22×C3
hypercenter#41D3×AGL(1,𝔽7)
hypocenterC3×C7C2×C3×H(5,𝔽2)
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2 ◁ #41

3756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×H(5,𝔽2)×AGL(1,𝔽7), AGL(1,𝔽7)×#4822, AGL(1,𝔽7)×#5198
maximal normal subgroup ofD3×H(5,𝔽2)×AGL(1,𝔽7), AGL(1,𝔽7)×#4822, AGL(1,𝔽7)×#5198

GAP

Past the SmallGroups library coverage — no SmallGroups id.