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AGL(1,𝔽43) #14268577

order1806
isoclinismisoclinic class of AGL(1,𝔽43)
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

affine general linearAGL(1,𝔽43)
unambiguous semidirect product(D43⋊C3)⋊C7
unambiguous semidirect product(D43⋊C7)⋊C3
unambiguous semidirect product((C43⋊C3)⋊C7)⋊C2

Splittings

Fitting, socle, derived, SylowC43 ⋊ C2×C3×C7
Hall(C43⋊C3)⋊C7 ⋊ C2
HallD43⋊C7 ⋊ C3
HallC43⋊C7 ⋊ C2×C3
HallD43⋊C3 ⋊ C7
HallC43⋊C3 ⋊ C2×C7
HallD43 ⋊ C3×C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC43C2×C3×C7
LCSG ▷ C43
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 43

Polycyclic presentation:

2,3,7,43|d^a=d^42,d^b=d^6,d^c=d^35

Conjugacy classes & character table

43 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽43), C7×AGL(1,𝔽43), #14268594⋊C7, …
maximal normal subgroup ofC2×AGL(1,𝔽43), C7×AGL(1,𝔽43), C13×AGL(1,𝔽43), …
maximal quotient of((C43⋊C3)⋊C4)⋊C7, C2×AGL(1,𝔽43), (D43⋊C3)⋊C49, …
automorphism group ofD43, C43⋊C3, D43⋊C3, …
holomorph ofC43

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1806, 1);