Finite Group Databasebeta

← Prev (#28330855) Next (#28330857) →

C29×#261⋊C9 #28330856

order13572
isoclinismisoclinic class of AGL(1,𝔽13)
automorphism?
homologyAbelianization (H1) = C4×C9×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×#261⋊C9
unambiguous semidirect product#261⋊(C9×C29)
unambiguous semidirect product(C29×#261)⋊C9

Splittings

derived, SylowC13 ⋊ C4×C9×C29
HallC29×C13⋊C9 ⋊ C4
HallC29×#261 ⋊ C9
HallC13×C29 ⋊ C4×C9
HallC13⋊C9 ⋊ C4×C29
Hall#261 ⋊ C9×C29

Subgroups

subgroupG/H
center, hypercenterC3×C29AGL(1,𝔽13)
commutator, hypocenterC13C4×C9×C29
FrattiniC3C29×AGL(1,𝔽13)
Fitting, socleC3×C13×C29C3×C4
prime radicalC3×D13×C29C2×C3
cosocleC3×D13C2×C3×C29
LCSG ▷ C13
UCSC1 ◁ C3×C29

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3393

Conjugacy classes & character table

1131 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13572, 14);