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C2×C3⋊AGL(1,𝔽71) #44447165

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

Aliases

direct productC2×C3⋊AGL(1,𝔽71)
unambiguous semidirect product(C2×C3)⋊AGL(1,𝔽71)
unambiguous semidirect product(C2×C3⋊(D71⋊C5))⋊C7
unambiguous semidirect product(C2×(C71⋊C5)⋊C7)⋊D3
unambiguous semidirect product(C2×C3⋊(D71⋊C7))⋊C5

Splittings

Fitting, socleC2×C3×C71 ⋊ C2×C5×C7
derived, HallC3×C71 ⋊ C22×C5×C7
HallC3×(C71⋊C5)⋊C7 ⋊ C22
HallC2×C3⋊(D71⋊C7) ⋊ C5
HallC2×C3⋊(D71⋊C5) ⋊ C7
Hall(C71⋊C5)⋊C7 ⋊ C2×D3
HallC3×C71⋊C7 ⋊ C22×C5
HallC3×C71⋊C5 ⋊ C22×C7
HallC2×D213 ⋊ C5×C7
HallC71⋊C7 ⋊ C2×C5×D3
HallC71⋊C5 ⋊ C2×D3×C7
SylowC71 ⋊ C2×C5×D3×C7
SylowC3 ⋊ C2×AGL(1,𝔽71)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊AGL(1,𝔽71)
commutator, cosocle, hypocenterC3×C71C22×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C71C2×C5×C7
LCSG ▷ C3×C71
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 426

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 53);