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AGL(1,𝔽7)×D143 #26046479

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

Aliases

direct productAGL(1,𝔽7)×D143
unambiguous semidirect productD7⋊(C3×D143)
unambiguous semidirect product(C11×AGL(1,𝔽7))⋊D13
unambiguous semidirect product(C13×AGL(1,𝔽7))⋊D11

Splittings

Fitting, socle, derived, HallC7×C11×C13 ⋊ C22×C3
HallD7×D143 ⋊ 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) ⋊ C2×D143
SylowC13 ⋊ D11×AGL(1,𝔽7)
SylowC11 ⋊ D13×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×D143

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

511 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×C11⋊(D13⋊C3), C3×AGL(1,𝔽7)×D143, C3⋊AGL(1,𝔽7)×D143, …
maximal normal subgroup ofAGL(1,𝔽7)×C11⋊(D13⋊C3), C3×AGL(1,𝔽7)×D143
maximal quotient ofD7⋊C9×D143, C3×AGL(1,𝔽7)×D143, C3⋊AGL(1,𝔽7)×D143, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 69);