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C7×D13×AGL(1,𝔽7) #21439591

order7644
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D13×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C7×D13)
unambiguous semidirect product(ΓL(1,𝔽8)×D13)⋊(C2×C7)
unambiguous semidirect product(C13×AGL(1,𝔽7))⋊(C2×C7)
unambiguous semidirect product(ΓL(1,𝔽8)⋊D13)⋊(C2×C7)

Splittings

Fitting, socle, HallC72×C13 ⋊ C22×C3
derivedC7×C13 ⋊ C22×C3×C7
HallC7×D7×D13 ⋊ C3
HallC7×C13×ΓL(1,𝔽8) ⋊ C22
HallC7×ΓL(1,𝔽8) ⋊ C2×D13
SylowC72 ⋊ C2×C3×D13
SylowC13 ⋊ C2×C7×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC7D13×AGL(1,𝔽7)
commutator, hypocenterC7×C13C22×C3×C7
FrattiniC1G
Fitting, socleC72×C13C22×C3
LCSG ▷ C7×C13
UCSC1 ◁ C7

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

392 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×AGL(1,𝔽7)×D13⋊C3, AGL(1,𝔽7)×#10587716, AGL(1,𝔽7)×#10587717, …
maximal normal subgroup ofC7×AGL(1,𝔽7)×D13⋊C3, AGL(1,𝔽7)×#10587716, AGL(1,𝔽7)×#10587717, …
maximal quotient ofC7×D13×D7⋊C9, C3×C7×D13×AGL(1,𝔽7), C7×D13×C3⋊AGL(1,𝔽7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 160);