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C3×C17×ΓL(1,𝔽8)×C29 #44526919

order31059
automorphism?
homologyAbelianization (H1) = C32×C17×C29 · Schur multiplier (H2) = C3

Aliases

direct productC3×C17×ΓL(1,𝔽8)×C29
unambiguous semidirect productC7⋊(C32×C17×C29)
unambiguous semidirect product(C3×C7)⋊(C3×C17×C29)
unambiguous semidirect product(C7×C17)⋊(C32×C29)
unambiguous semidirect product(C7×C29)⋊(C32×C17)
unambiguous semidirect product(C3×C7×C17)⋊(C3×C29)
unambiguous semidirect product(C3×C7×C29)⋊(C3×C17)
unambiguous semidirect product(C7×C17×C29)⋊C32
unambiguous semidirect product(C3×C7×C17×C29)⋊C3

Splittings

Fitting, socleC3×C7×C17×C29 ⋊ C3
derived, SylowC7 ⋊ C32×C17×C29
HallC7×C17×C29 ⋊ C32
HallC7×C29 ⋊ C32×C17
HallC7×C17 ⋊ C32×C29

Subgroups

subgroupG/H
center, hypercenterC3×C17×C29ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C32×C17×C29
FrattiniC1G
Fitting, socleC3×C7×C17×C29C3
LCSG ▷ C7
UCSC1 ◁ C3×C17×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10353

Conjugacy classes & character table

7395 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31059, 6);