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C3×C7×AGL(1,𝔽31) #34086173

order19530
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×AGL(1,𝔽31)
unambiguous semidirect product(D31⋊C3)⋊(C3×C5×C7)
unambiguous semidirect product(D31⋊C5)⋊(C32×C7)
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(C2×C3×C7)
unambiguous semidirect product(C3×D31⋊C3)⋊(C5×C7)
unambiguous semidirect product(C3×D31⋊C5)⋊(C3×C7)
unambiguous semidirect product(C3×C7×D31⋊C3)⋊C5

Splittings

Fitting, socleC3×C7×C31 ⋊ C2×C3×C5
derived, SylowC31 ⋊ C2×C32×C5×C7
HallC3×C7×(C31⋊C3)⋊C5 ⋊ C2
HallC3×C7×D31⋊C3 ⋊ C5
HallC7×D31⋊C5 ⋊ C32
HallC3×C7×C31⋊C3 ⋊ C2×C5
HallC3×(C31⋊C3)⋊C5 ⋊ C2×C7
HallC7×ΓL(1,𝔽32) ⋊ C2×C32
HallC3×D31⋊C3 ⋊ C5×C7
HallC7×D31 ⋊ C32×C5
HallD31⋊C5 ⋊ C32×C7
HallC3×C31⋊C3 ⋊ C2×C5×C7
HallC7×C31 ⋊ C2×C32×C5
HallΓL(1,𝔽32) ⋊ C2×C32×C7
HallD31 ⋊ C32×C5×C7

Subgroups

subgroupG/H
center, hypercenterC3×C7AGL(1,𝔽31)
commutator, cosocle, hypocenterC31C2×C32×C5×C7
FrattiniC1G
Fitting, socleC3×C7×C31C2×C3×C5
LCSG ▷ C31
UCSC1 ◁ C3×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 651

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 78);