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C3×C4×(C43⋊C3)⋊C7 #24925492

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

Aliases

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

Splittings

FittingC3×C4×C43 ⋊ C3×C7
derived, SylowC43 ⋊ C32×C4×C7
HallC3×C4×C43⋊C3 ⋊ C7
HallC4×C43⋊C7 ⋊ C32
HallC3×C43⋊C3 ⋊ C4×C7
HallC43⋊C7 ⋊ C32×C4
HallC4×C43 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC3×C4(C43⋊C3)⋊C7
commutator, hypocenterC43C32×C4×C7
FrattiniC2C2×C3×(C43⋊C3)⋊C7
FittingC3×C4×C43C3×C7
socleC2×C3×C43C2×C3×C7
prime radicalC2×C3×(C43⋊C3)⋊C7C2
cosocleC2×C43C2×C32×C7
LCSG ▷ C43
UCSC1 ◁ C3×C4

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

276 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 84);