Finite Group Databasebeta

← Prev (#35208497) Next (#35208499) →

C17×ΓL(1,𝔽8)⋊D29 #35208498

order20706
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×ΓL(1,𝔽8)⋊D29
unambiguous semidirect productΓL(1,𝔽8)⋊(C17×D29)
unambiguous semidirect productC29⋊(C17×AGL(1,𝔽7))
unambiguous semidirect productD203⋊(C3×C17)
unambiguous semidirect product(C17×D203)⋊C3

Splittings

Fitting, socle, HallC7×C17×C29 ⋊ C2×C3
derived, HallC7×C29 ⋊ C2×C3×C17
HallC17×ΓL(1,𝔽8)×C29 ⋊ C2
HallC17×D203 ⋊ C3
HallΓL(1,𝔽8)×C29 ⋊ C2×C17
HallC17×C29 ⋊ AGL(1,𝔽7)
HallD203 ⋊ C3×C17
HallC17×ΓL(1,𝔽8) ⋊ D29
HallC7×C17 ⋊ C3×D29
SylowC29 ⋊ C17×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C17×D29
SylowC7 ⋊ C3×C17×D29

Subgroups

subgroupG/H
center, hypercenterC17ΓL(1,𝔽8)⋊D29
commutator, cosocle, hypocenterC7×C29C2×C3×C17
FrattiniC1G
Fitting, socleC7×C17×C29C2×C3
LCSG ▷ C7×C29
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3451

Conjugacy classes & character table

1309 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20706, 30);