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D13×C11⋊AGL(1,𝔽7) #26046486

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

Aliases

direct productD13×C11⋊AGL(1,𝔽7)
unambiguous semidirect product(ΓL(1,𝔽8)×D13)⋊D11

Splittings

Fitting, socle, derived, HallC7×C11×C13 ⋊ C22×C3
HallD13×D77 ⋊ C3
HallC11×C13×ΓL(1,𝔽8) ⋊ C22
HallC13×ΓL(1,𝔽8) ⋊ C2×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×D13
HallC11×C13 ⋊ C2×AGL(1,𝔽7)
HallC7×C13 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D13
HallΓL(1,𝔽8) ⋊ D11×D13
SylowC13 ⋊ C2×C11⋊AGL(1,𝔽7)
SylowC11 ⋊ D13×AGL(1,𝔽7)
SylowC7 ⋊ C3×D11×D13

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C13C22×C3
LCSG ▷ C7×C11×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13⋊C3×C11⋊AGL(1,𝔽7), C3×D13×C11⋊AGL(1,𝔽7), D13×C3⋊(C11⋊AGL(1,𝔽7)), …
maximal normal subgroup ofD13⋊C3×C11⋊AGL(1,𝔽7), C3×D13×C11⋊AGL(1,𝔽7)
maximal quotient ofD13×C11⋊(D7⋊C9), C3×D13×C11⋊AGL(1,𝔽7), D13×C3⋊(C11⋊AGL(1,𝔽7)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 76);