Finite Group Databasebeta

C32×#11760453 #23748612

order9477
automorphism?
homologyAbelianization (H1) = C35 · Schur multiplier (H2) = C39

Aliases

direct productC32×#11760453

Splittings

FittingC33×C9×C13 ⋊ C3
SylowC13 ⋊ C32×#737

Subgroups

subgroupG/H
centerC32×C9C3×C13⋊C3
commutator, cosocleC3×C13C35
FrattiniC3C34×C13⋊C3
FittingC33×C9×C13C3
socleC33×C13C33
prime radicalC32×C32⋊(C13⋊C3)C3
hypercenterC33×C9C13⋊C3
hypocenterC13C32×#737
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C32×C9 ◁ C33×C9

5804 conjugacy classes of subgroups; only the 2920 normal subgroups are shown.

normal subgroups only

This group has 5804 conjugacy classes of subgroups — too many to draw. Only its 2920 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

1269 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9477, 4021);