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C2×(D43⋊C7)⋊C9 #24925440

order10836
automorphism?
homologyAbelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×(D43⋊C7)⋊C9
unambiguous semidirect product(D43⋊C7)⋊(C2×C9)
unambiguous semidirect product(D43⋊C9)⋊(C2×C7)
unambiguous semidirect product(C2×D43⋊C7)⋊C9
unambiguous semidirect product(C2×D43⋊C9)⋊C7
unambiguous semidirect product((C43⋊C7)⋊C9)⋊C22
unambiguous semidirect product(C2×(C43⋊C7)⋊C9)⋊C2

Splittings

derived, SylowC43 ⋊ C22×C7×C9
Hall(C43⋊C7)⋊C9 ⋊ C22
HallC2×D43⋊C9 ⋊ C7
HallC2×D43⋊C7 ⋊ C9
HallC43⋊C9 ⋊ C22×C7
HallC43⋊C7 ⋊ C22×C9
HallC2×D43 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3AGL(1,𝔽43)
commutator, hypocenterC43C22×C7×C9
FrattiniC3C2×AGL(1,𝔽43)
Fitting, socleC2×C3×C43C2×C3×C7
prime radicalC2×C3×D43⋊C7C3
cosocleC3×C43C22×C3×C7
LCSG ▷ C43
UCSC1 ◁ C2×C3

60 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, 32);