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C13×D7×AGL(1,𝔽7) #21439635

order7644
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×D7×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C13×D7)
unambiguous semidirect product(C7×AGL(1,𝔽7))⋊(C2×C13)
unambiguous semidirect product(D7×ΓL(1,𝔽8))⋊(C2×C13)
unambiguous semidirect product(ΓL(1,𝔽8)⋊D7)⋊(C2×C13)

Splittings

Fitting, socle, HallC72×C13 ⋊ C22×C3
derived, SylowC72 ⋊ C22×C3×C13
HallC13×D72 ⋊ C3
HallC7×C13×ΓL(1,𝔽8) ⋊ C22
HallD72 ⋊ C3×C13
HallC7×ΓL(1,𝔽8) ⋊ C22×C13

Subgroups

subgroupG/H
center, hypercenterC13D7×AGL(1,𝔽7)
commutator, hypocenterC72C22×C3×C13
FrattiniC1G
Fitting, socleC72×C13C22×C3
LCSG ▷ C72
UCSC1 ◁ C13

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

455 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×AGL(1,𝔽7)2, AGL(1,𝔽7)×#10587720, AGL(1,𝔽7)×#10587721, …
maximal normal subgroup ofC13×AGL(1,𝔽7)2, AGL(1,𝔽7)×#10587720, AGL(1,𝔽7)×#10587721, …
maximal quotient ofC13×D7×D7⋊C9, C3×C13×D7×AGL(1,𝔽7), C13×D7×C3⋊AGL(1,𝔽7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 204);