Finite Group Databasebeta

← Prev (#30654999) Next (#30655001) →

C5×C7×#261⋊C9 #30655000

order16380
isoclinismisoclinic class of AGL(1,𝔽13)
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×#261⋊C9
unambiguous semidirect product#261⋊(C5×C7×C9)
unambiguous semidirect product(C5×#261)⋊(C7×C9)

Splittings

derived, SylowC13 ⋊ C4×C5×C7×C9
HallC5×C7×C13⋊C9 ⋊ C4
HallC5×C7×#261 ⋊ C9
HallC7×C13⋊C9 ⋊ C4×C5
HallC5×C13⋊C9 ⋊ C4×C7
HallC5×C7×C13 ⋊ C4×C9
HallC7×#261 ⋊ C5×C9
HallC5×#261 ⋊ C7×C9
HallC13⋊C9 ⋊ C4×C5×C7
HallC7×C13 ⋊ C4×C5×C9
HallC5×C13 ⋊ C4×C7×C9
Hall#261 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7AGL(1,𝔽13)
commutator, hypocenterC13C4×C5×C7×C9
FrattiniC3C5×C7×AGL(1,𝔽13)
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×C5×C7×D13C2×C3
cosocleC3×D13C2×C3×C5×C7
LCSG ▷ C13
UCSC1 ◁ C3×C5×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4095

Conjugacy classes & character table

1365 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 50);