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C11×D13×AGL(1,𝔽7) #26046468

order12012
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D13×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C11×D13)
unambiguous semidirect product(ΓL(1,𝔽8)×D13)⋊(C2×C11)
unambiguous semidirect product(C13×AGL(1,𝔽7))⋊(C2×C11)
unambiguous semidirect product(ΓL(1,𝔽8)⋊D13)⋊(C2×C11)

Splittings

Fitting, socle, HallC7×C11×C13 ⋊ C22×C3
derived, HallC7×C13 ⋊ C22×C3×C11
HallC11×D7×D13 ⋊ C3
HallC11×C13×ΓL(1,𝔽8) ⋊ C22
HallD7×D13 ⋊ C3×C11
HallC13×ΓL(1,𝔽8) ⋊ C22×C11
HallC11×ΓL(1,𝔽8) ⋊ C2×D13
HallC11×C13 ⋊ C2×AGL(1,𝔽7)
HallC7×C11 ⋊ C2×C3×D13
HallΓL(1,𝔽8) ⋊ C2×C11×D13
SylowC13 ⋊ C2×C11×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×C11×D13

Subgroups

subgroupG/H
center, hypercenterC11D13×AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C13C22×C3×C11
FrattiniC1G
Fitting, socleC7×C11×C13C22×C3
LCSG ▷ C7×C13
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

616 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×AGL(1,𝔽7)×D13⋊C3, C3×C11×D13×AGL(1,𝔽7), C11×D13×C3⋊AGL(1,𝔽7), …
maximal normal subgroup ofC11×AGL(1,𝔽7)×D13⋊C3, C3×C11×D13×AGL(1,𝔽7)
maximal quotient ofC11×D13×D7⋊C9, C3×C11×D13×AGL(1,𝔽7), C11×D13×C3⋊AGL(1,𝔽7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 58);