Finite Group Databasebeta

← Prev (#24902866) Next (#24902868) →

C9×AGL(1,𝔽5)×C59 #24902867

order10620
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C9×C59 · Schur multiplier (H2) = C1

Aliases

direct productC9×AGL(1,𝔽5)×C59

Splittings

Fitting, HallC5×C9×C59 ⋊ C4
derived, SylowC5 ⋊ C4×C9×C59
HallC5×C59 ⋊ C4×C9
HallC5×C9 ⋊ C4×C59

Subgroups

subgroupG/H
center, hypercenterC9×C59AGL(1,𝔽5)
commutator, hypocenterC5C4×C9×C59
FrattiniC3C3×AGL(1,𝔽5)×C59
FittingC5×C9×C59C4
socleC3×C5×C59C3×C4
prime radicalC3×D5×C59C2×C3
cosocleC3×D5C2×C3×C59
LCSG ▷ C5
UCSC1 ◁ C9×C59

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2655 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10620, 10);