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C2×C3×AGL(1,𝔽71) #44447164

order29820
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×AGL(1,𝔽71)
unambiguous semidirect product(D71⋊C5)⋊(C2×C3×C7)
unambiguous semidirect product(D71⋊C7)⋊(C2×C3×C5)
unambiguous semidirect product(C2×D71⋊C5)⋊(C3×C7)
unambiguous semidirect product(C2×D71⋊C7)⋊(C3×C5)
unambiguous semidirect product((C71⋊C5)⋊C7)⋊(C22×C3)
unambiguous semidirect product(C2×C3×D71⋊C5)⋊C7
unambiguous semidirect product(C2×(C71⋊C5)⋊C7)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D71⋊C7)⋊C5

Splittings

Fitting, socleC2×C3×C71 ⋊ C2×C5×C7
derived, SylowC71 ⋊ C22×C3×C5×C7
HallC3×(C71⋊C5)⋊C7 ⋊ C22
HallC2×C3×D71⋊C7 ⋊ C5
HallC2×C3×D71⋊C5 ⋊ C7
Hall(C71⋊C5)⋊C7 ⋊ C22×C3
HallC2×D71⋊C7 ⋊ C3×C5
HallC3×C71⋊C7 ⋊ C22×C5
HallC2×D71⋊C5 ⋊ C3×C7
HallC3×C71⋊C5 ⋊ C22×C7
HallC2×C3×D71 ⋊ C5×C7
HallC71⋊C7 ⋊ C22×C3×C5
HallC71⋊C5 ⋊ C22×C3×C7
HallC2×D71 ⋊ C3×C5×C7
HallC3×C71 ⋊ C22×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3AGL(1,𝔽71)
commutator, cosocle, hypocenterC71C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C71C2×C5×C7
LCSG ▷ C71
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 426

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 52);