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AGL(1,𝔽7)×C197 #22552020

order8274
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C3×C197 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽7)×C197
unambiguous semidirect productD7⋊(C3×C197)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C197)
unambiguous semidirect product(D7×C197)⋊C3

Splittings

Fitting, socle, HallC7×C197 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C197
HallΓL(1,𝔽8)×C197 ⋊ C2
HallD7×C197 ⋊ C3
HallΓL(1,𝔽8) ⋊ C2×C197
HallD7 ⋊ C3×C197

Subgroups

subgroupG/H
center, hypercenterC197AGL(1,𝔽7)
commutator, hypocenterC7C2×C3×C197
FrattiniC1G
Fitting, socleC7×C197C2×C3
LCSG ▷ C7
UCSC1 ◁ C197

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1379 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽7)×D197, C2×AGL(1,𝔽7)×C197, C3×AGL(1,𝔽7)×C197, …
maximal normal subgroup ofAGL(1,𝔽7)×D197, C2×AGL(1,𝔽7)×C197, C3×AGL(1,𝔽7)×C197
maximal quotient ofΓL(1,𝔽8)⋊C4×C197, C2×AGL(1,𝔽7)×C197, D7⋊C9×C197, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8274, 15);