Finite Group Databasebeta

← Prev (#72230258) Next (#72230260) →

AGL(1,𝔽7)×#546 #72230259

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

Aliases

direct productAGL(1,𝔽7)×#546

Splittings

FittingC7×#546 ⋊ C2×C3
HallD7×#546 ⋊ C3
HallΓL(1,𝔽8) ⋊ C2×#546
SylowC7 ⋊ C2×C3×#546

Subgroups

subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽7)
commutator, socle, cosocleC22×C7C25×C3
FittingC7×#546C2×C3
hypercenter#546AGL(1,𝔽7)
hypocenterC7C2×C3×#546
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ #546

3800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 112

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×#3484, AGL(1,𝔽7)×#3532, AGL(1,𝔽7)×#3490
maximal normal subgroup ofAGL(1,𝔽7)×#3484, AGL(1,𝔽7)×#3532, AGL(1,𝔽7)×#3490

GAP

Past the SmallGroups library coverage — no SmallGroups id.