Finite Group Databasebeta

← Prev (#30655283) Next (#30655285) →

C5×ΓL(1,𝔽8)⋊AGL(1,𝔽13) #30655284

order16380
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×ΓL(1,𝔽8)⋊AGL(1,𝔽13)
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×AGL(1,𝔽13))
unambiguous semidirect product#11763979⋊(C3×C5)
unambiguous semidirect product(ΓL(1,𝔽8)⋊#261)⋊(C3×C5)
unambiguous semidirect product#11763984⋊(C3×C5)
unambiguous semidirect product#11763985⋊(C3×C5)
unambiguous semidirect product(C5×#11763985)⋊C3
unambiguous semidirect product(C5×#11763984)⋊C3
unambiguous semidirect product(C5×ΓL(1,𝔽8)⋊#261)⋊C3
unambiguous semidirect product(C5×#11763979)⋊C3

Splittings

Fitting, socle, HallC5×C7×C13 ⋊ C32×C4
derived, HallC7×C13 ⋊ C32×C4×C5
HallC5×ΓL(1,𝔽8)×C13⋊C3 ⋊ C4
HallC5×C7⋊#261 ⋊ C32
HallΓL(1,𝔽8)×C13⋊C3 ⋊ C4×C5
HallC7⋊#261 ⋊ C32×C5
HallC5×C13 ⋊ C3×ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ C3×AGL(1,𝔽13)
SylowC13 ⋊ C3×C5×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C5×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)⋊AGL(1,𝔽13)
commutator, hypocenterC7×C13C32×C4×C5
FrattiniC1G
Fitting, socleC5×C7×C13C32×C4
prime radicalC5×ΓL(1,𝔽8)×D13⋊C3C2
cosocleC7×D13C2×C32×C5
LCSG ▷ C7×C13
UCSC1 ◁ C5

144 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 455

Conjugacy classes & character table

235 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 334);