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#131×AGL(1,𝔽7) #13057483

order1344
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct product#131×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×#131)

Splittings

FittingC7×#131 ⋊ C2×C3
HallD7×#131 ⋊ C3
HallΓL(1,𝔽8) ⋊ C2×#131
SylowC7 ⋊ C2×C3×#131

Subgroups

subgroupG/H
centerC8C22×AGL(1,𝔽7)
commutator, socleC2×C7C23×C3×C4
FrattiniC4C23×AGL(1,𝔽7)
FittingC7×#131C2×C3
prime radical#41×AGL(1,𝔽7)C2
cosocleC4×C7C24×C3
hypercenter#131AGL(1,𝔽7)
hypocenterC7C2×C3×#131
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C8 ◁ #131

532 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 112

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×#444, AGL(1,𝔽7)×#568, AGL(1,𝔽7)×#443, …
maximal normal subgroup ofAGL(1,𝔽7)×#444, AGL(1,𝔽7)×#568, AGL(1,𝔽7)×#443, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 6772);