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C2×C13×C29×AGL(1,𝔽7) #44539886

order31668
automorphism?
homologyAbelianization (H1) = C22×C3×C13×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×C29×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C2×C3×C13×C29)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C13×C29)
unambiguous semidirect product(C2×D7)⋊(C3×C13×C29)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C13×C29)
unambiguous semidirect product(C2×D7×C29)⋊(C3×C13)

Splittings

Fitting, socleC2×C7×C13×C29 ⋊ C2×C3
derived, SylowC7 ⋊ C22×C3×C13×C29
HallC2×C13×D7×C29 ⋊ C3
HallC13×ΓL(1,𝔽8)×C29 ⋊ C22
HallC7×C13×C29 ⋊ C22×C3
HallC2×D7×C29 ⋊ C3×C13
HallΓL(1,𝔽8)×C29 ⋊ C22×C13
HallC2×C13×D7 ⋊ C3×C29
HallC13×ΓL(1,𝔽8) ⋊ C22×C29
HallC7×C29 ⋊ C22×C3×C13
HallC7×C13 ⋊ C22×C3×C29
HallC2×D7 ⋊ C3×C13×C29
HallΓL(1,𝔽8) ⋊ C22×C13×C29

Subgroups

subgroupG/H
center, hypercenterC2×C13×C29AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C22×C3×C13×C29
FrattiniC1G
Fitting, socleC2×C7×C13×C29C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C13×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5278

Conjugacy classes & character table

5278 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 181);