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AGL(1,𝔽7)×#534 #72230255

order2688
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C29

Aliases

direct productAGL(1,𝔽7)×#534

Splittings

FittingC7×#534 ⋊ C2×C3
HallD7×#534 ⋊ C3
HallΓL(1,𝔽8) ⋊ C2×#534
SylowC7 ⋊ C2×C3×#534

Subgroups

subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽7)
commutator, socle, cosocleC22×C7C25×C3
FittingC7×#534C2×C3
hypercenter#534AGL(1,𝔽7)
hypocenterC7C2×C3×#534
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ #534

3968 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 112

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×#3484, AGL(1,𝔽7)×#2021, AGL(1,𝔽7)×#3026, …
maximal normal subgroup ofAGL(1,𝔽7)×#3484, AGL(1,𝔽7)×#2021, AGL(1,𝔽7)×#3026, …
maximal quotient ofAGL(1,𝔽7)×#2403, AGL(1,𝔽7)×#2679

GAP

Past the SmallGroups library coverage — no SmallGroups id.