Finite Group Databasebeta

← Prev (#37590356) Next (#37590358) →

C9×AGL(1,𝔽5)×C137 #37590357

order24660
automorphism?
homologyAbelianization (H1) = C4×C9×C137 · Schur multiplier (H2) = C1

Aliases

direct productC9×AGL(1,𝔽5)×C137

Splittings

Fitting, HallC5×C9×C137 ⋊ C4
derived, SylowC5 ⋊ C4×C9×C137
HallC5×C137 ⋊ C4×C9
HallC5×C9 ⋊ C4×C137

Subgroups

subgroupG/H
center, hypercenterC9×C137AGL(1,𝔽5)
commutator, hypocenterC5C4×C9×C137
FrattiniC3C3×AGL(1,𝔽5)×C137
FittingC5×C9×C137C4
socleC3×C5×C137C3×C4
prime radicalC3×D5×C137C2×C3
cosocleC3×D5C2×C3×C137
LCSG ▷ C5
UCSC1 ◁ C9×C137

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6165

Conjugacy classes & character table

6165 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24660, 11);