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C13×AGL(1,𝔽43) #37553544

order23478
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×AGL(1,𝔽43)
unambiguous semidirect product(D43⋊C3)⋊(C7×C13)
unambiguous semidirect product(D43⋊C7)⋊(C3×C13)
unambiguous semidirect product((C43⋊C3)⋊C7)⋊(C2×C13)
unambiguous semidirect product(C13×D43⋊C3)⋊C7

Splittings

Fitting, socle, HallC13×C43 ⋊ C2×C3×C7
derived, SylowC43 ⋊ C2×C3×C7×C13
HallC13×(C43⋊C3)⋊C7 ⋊ C2
HallC13×D43⋊C7 ⋊ C3
HallC13×C43⋊C7 ⋊ C2×C3
HallC13×D43⋊C3 ⋊ C7
HallC13×C43⋊C3 ⋊ C2×C7
HallC13×D43 ⋊ C3×C7
Hall(C43⋊C3)⋊C7 ⋊ C2×C13
HallD43⋊C7 ⋊ C3×C13
HallC43⋊C7 ⋊ C2×C3×C13
HallD43⋊C3 ⋊ C7×C13
HallC43⋊C3 ⋊ C2×C7×C13
HallD43 ⋊ C3×C7×C13

Subgroups

subgroupG/H
center, hypercenterC13AGL(1,𝔽43)
commutator, cosocle, hypocenterC43C2×C3×C7×C13
FrattiniC1G
Fitting, socleC13×C43C2×C3×C7
LCSG ▷ C43
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 559

Conjugacy classes & character table

559 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23478, 133);