Finite Group Databasebeta

C3×C9⋊C9×C37⋊C3 #41007489

order26973
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C36

Aliases

direct productC3×C9⋊C9×C37⋊C3

Splittings

FittingC3×C37×C9⋊C9 ⋊ C3
SylowC37 ⋊ C32×C9⋊C9

Subgroups

subgroupG/H
centerC33C32×C37⋊C3
commutatorC3×C37C33×C9
FrattiniC32C33×C37⋊C3
FittingC3×C37×C9⋊C9C3
socleC33×C37C33
prime radicalC33×C37⋊C3C32
cosocleC32×C37C34
hypercenterC3×C9⋊C9C37⋊C3
hypocenterC37C32×C9⋊C9
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C33 ◁ C3×C9⋊C9

1484 conjugacy classes of subgroups; only the 652 normal subgroups are shown.

normal subgroups only

This group has 1484 conjugacy classes of subgroups — too many to draw. Only its 652 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Conjugacy classes & character table

1485 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 3260);