Finite Group Databasebeta

← Prev (#13057339) Next (#13057341) →

#121×AGL(1,𝔽7) #13057340

order1344
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct product#121×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×#121)
unambiguous semidirect product(D7×#121)⋊C3

Splittings

FittingC7×#121 ⋊ C2×C3
HallD7×#121 ⋊ C3
HallΓL(1,𝔽8) ⋊ C2×#121
SylowC7 ⋊ C2×C3×#121

Subgroups

subgroupG/H
center, FrattiniC22C23×AGL(1,𝔽7)
commutator, socle, cosocleC22×C7C24×C3
FittingC7×#121C2×C3
hypercenter#121AGL(1,𝔽7)
hypocenterC7C2×C3×#121
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ #121

852 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 112

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×#525, AGL(1,𝔽7)×#535, AGL(1,𝔽7)×#532, …
maximal normal subgroup ofAGL(1,𝔽7)×#525, AGL(1,𝔽7)×#535, AGL(1,𝔽7)×#532, …
maximal quotient ofAGL(1,𝔽7)×#386, AGL(1,𝔽7)×#469, AGL(1,𝔽7)×#392, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 6629);