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C2×C3×AGL(1,𝔽43) #24925549

order10836
automorphism?
homologyAbelianization (H1) = C22×C32×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×AGL(1,𝔽43)
unambiguous semidirect product(D43⋊C3)⋊(C2×C3×C7)
unambiguous semidirect product(C2×D43⋊C3)⋊(C3×C7)
unambiguous semidirect product(D43⋊C7)⋊(C2×C32)
unambiguous semidirect product((C43⋊C3)⋊C7)⋊(C22×C3)
unambiguous semidirect product(C2×D43⋊C7)⋊C32
unambiguous semidirect product(C2×C3×D43⋊C3)⋊C7
unambiguous semidirect product(C2×(C43⋊C3)⋊C7)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D43⋊C7)⋊C3

Splittings

Fitting, socleC2×C3×C43 ⋊ C2×C3×C7
derived, SylowC43 ⋊ C22×C32×C7
HallC3×(C43⋊C3)⋊C7 ⋊ C22
HallC2×C3×D43⋊C3 ⋊ C7
HallC2×D43⋊C7 ⋊ C32
HallC3×C43⋊C3 ⋊ C22×C7
HallC43⋊C7 ⋊ C22×C32
HallC2×D43 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3AGL(1,𝔽43)
commutator, cosocle, hypocenterC43C22×C32×C7
FrattiniC1G
Fitting, socleC2×C3×C43C2×C3×C7
LCSG ▷ C43
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

258 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 141);