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C3×((C43⋊C3)⋊C4)⋊C7 #24925489

order10836
automorphism?
homologyAbelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×((C43⋊C3)⋊C4)⋊C7
unambiguous semidirect product((C43⋊C3)⋊C4)⋊(C3×C7)
unambiguous semidirect product((C43⋊C3)⋊C7)⋊(C3×C4)
unambiguous semidirect product(Dic43⋊C7)⋊C32
unambiguous semidirect product(C3×(C43⋊C3)⋊C4)⋊C7
unambiguous semidirect product(C3×Dic43⋊C7)⋊C3

Splittings

derived, SylowC43 ⋊ C32×C4×C7
HallC3×(C43⋊C3)⋊C7 ⋊ C4
HallC3×(C43⋊C3)⋊C4 ⋊ C7
HallDic43⋊C7 ⋊ C32
HallC3×C43⋊C3 ⋊ C4×C7
HallC43⋊C7 ⋊ C32×C4
HallDic43 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3AGL(1,𝔽43)
commutator, hypocenterC43C32×C4×C7
FrattiniC2C3×AGL(1,𝔽43)
Fitting, socleC2×C3×C43C2×C3×C7
prime radicalC2×C3×(C43⋊C3)⋊C7C2
cosocleC2×C43C2×C32×C7
LCSG ▷ C43
UCSC1 ◁ C2×C3

72 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, 81);