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AGL(1,𝔽7)×#1715 #72259506

order5376
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C23×C8

Aliases

direct productAGL(1,𝔽7)×#1715

Splittings

FittingC7×#1715 ⋊ C2×C3
HallD7×#1715 ⋊ C3
HallΓL(1,𝔽8) ⋊ C2×#1715
SylowC7 ⋊ C2×C3×#1715

Subgroups

subgroupG/H
centerC22#127×AGL(1,𝔽7)
commutator, cosocleC42×C7C24×C3
FrattiniC42C23×AGL(1,𝔽7)
FittingC7×#1715C2×C3
socleC22×C7C2×C3×#127
prime radicalAGL(1,𝔽7)×#493C2
hypercenter#1715AGL(1,𝔽7)
hypocenterC7C2×C3×#1715
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C42 ◁ #1715

2060 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×#19745
maximal normal subgroup ofAGL(1,𝔽7)×#19745

GAP

Past the SmallGroups library coverage — no SmallGroups id.