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C13×D11×AGL(1,𝔽7) #26046469

order12012
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×D11×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C13×D11)
unambiguous semidirect product(D7×D11)⋊(C3×C13)
unambiguous semidirect product(ΓL(1,𝔽8)×D11)⋊(C2×C13)
unambiguous semidirect product(C11×AGL(1,𝔽7))⋊(C2×C13)
unambiguous semidirect product(C11⋊AGL(1,𝔽7))⋊(C2×C13)

Splittings

Fitting, socle, HallC7×C11×C13 ⋊ C22×C3
derived, HallC7×C11 ⋊ C22×C3×C13
HallC13×D7×D11 ⋊ C3
HallC11×C13×ΓL(1,𝔽8) ⋊ C22
HallD7×D11 ⋊ C3×C13
HallC13×ΓL(1,𝔽8) ⋊ C2×D11
HallC11×ΓL(1,𝔽8) ⋊ C22×C13
HallC11×C13 ⋊ C2×AGL(1,𝔽7)
HallC7×C13 ⋊ C2×C3×D11
HallΓL(1,𝔽8) ⋊ C2×C13×D11
SylowC11 ⋊ C2×C13×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×C13×D11

Subgroups

subgroupG/H
center, hypercenterC13D11×AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C11C22×C3×C13
FrattiniC1G
Fitting, socleC7×C11×C13C22×C3
LCSG ▷ C7×C11
UCSC1 ◁ C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

637 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×C13⋊C3×AGL(1,𝔽7), C3×C13×D11×AGL(1,𝔽7), C13×D11×C3⋊AGL(1,𝔽7), …
maximal normal subgroup ofD11×C13⋊C3×AGL(1,𝔽7), C3×C13×D11×AGL(1,𝔽7)
maximal quotient ofC13×D11×D7⋊C9, C3×C13×D11×AGL(1,𝔽7), C13×D11×C3⋊AGL(1,𝔽7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 59);