Finite Group Databasebeta

← Prev (#44418087) Next (#44418089) →

C17×ΓL(1,𝔽8)⋊D41 #44418088

order29274
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×ΓL(1,𝔽8)⋊D41
unambiguous semidirect productΓL(1,𝔽8)⋊(C17×D41)
unambiguous semidirect productC41⋊(C17×AGL(1,𝔽7))
unambiguous semidirect productD287⋊(C3×C17)
unambiguous semidirect product(C17×D287)⋊C3

Splittings

Fitting, socle, HallC7×C17×C41 ⋊ C2×C3
derived, HallC7×C41 ⋊ C2×C3×C17
HallC17×ΓL(1,𝔽8)×C41 ⋊ C2
HallC17×D287 ⋊ C3
HallΓL(1,𝔽8)×C41 ⋊ C2×C17
HallC17×C41 ⋊ AGL(1,𝔽7)
HallD287 ⋊ C3×C17
HallC17×ΓL(1,𝔽8) ⋊ D41
HallC7×C17 ⋊ C3×D41
SylowC41 ⋊ C17×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C17×D41
SylowC7 ⋊ C3×C17×D41

Subgroups

subgroupG/H
center, hypercenterC17ΓL(1,𝔽8)⋊D41
commutator, cosocle, hypocenterC7×C41C2×C3×C17
FrattiniC1G
Fitting, socleC7×C17×C41C2×C3
LCSG ▷ C7×C41
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4879

Conjugacy classes & character table

1819 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29274, 22);