Finite Group Databasebeta

C3×#22582564 #41007549

order26973
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C36

Aliases

direct productC3×#22582564

Splittings

FittingC33×C9×C37 ⋊ C3
SylowC37 ⋊ C3×#6893

Subgroups

subgroupG/H
centerC33C32×C37⋊C3
commutator, cosocleC32×C37C34
FrattiniC32C33×C37⋊C3
FittingC33×C9×C37C3
socleC33×C37C33
prime radicalC32×C32⋊(C37⋊C3)C3
hypercenterC33×C9C37⋊C3
hypocenterC37C3×#6893
LCSG ▷ C32×C37 ▷ C37
UCSC1 ◁ C33 ◁ C33×C9

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Conjugacy classes & character table

3069 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 3320);