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C3×AGL(1,𝔽71) #28415873

order14910
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×AGL(1,𝔽71)
unambiguous semidirect product(D71⋊C5)⋊(C3×C7)
unambiguous semidirect product(D71⋊C7)⋊(C3×C5)
unambiguous semidirect product(C3×D71⋊C5)⋊C7
unambiguous semidirect product((C71⋊C5)⋊C7)⋊(C2×C3)
unambiguous semidirect product(C3×D71⋊C7)⋊C5

Splittings

Fitting, socle, HallC3×C71 ⋊ C2×C5×C7
derived, SylowC71 ⋊ C2×C3×C5×C7
HallC3×(C71⋊C5)⋊C7 ⋊ C2
HallC3×D71⋊C7 ⋊ C5
Hall(C71⋊C5)⋊C7 ⋊ C2×C3
HallC3×D71⋊C5 ⋊ C7
HallC3×C71⋊C7 ⋊ C2×C5
HallC3×C71⋊C5 ⋊ C2×C7
HallD71⋊C7 ⋊ C3×C5
HallD71⋊C5 ⋊ C3×C7
HallC71⋊C7 ⋊ C2×C3×C5
HallC3×D71 ⋊ C5×C7
HallC71⋊C5 ⋊ C2×C3×C7
HallD71 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC3AGL(1,𝔽71)
commutator, cosocle, hypocenterC71C2×C3×C5×C7
FrattiniC1G
Fitting, socleC3×C71C2×C5×C7
LCSG ▷ C71
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 213

Conjugacy classes & character table

213 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽71), C2×C3×AGL(1,𝔽71)
maximal normal subgroup ofD3×AGL(1,𝔽71), C2×C3×AGL(1,𝔽71)
maximal quotient ofC3×(Dic71⋊C5)⋊C7, C2×C3×AGL(1,𝔽71)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14910, 36);