Finite Group Databasebeta

C3×#22582538 #41007497

order26973
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C34×C9

Aliases

direct productC3×#22582538

Splittings

SylowC37 ⋊ C3×#6887

Subgroups

subgroupG/H
centerC32×C9C3×C37⋊C3
commutatorC3×C37C33×C9
FrattiniC32C33×C37⋊C3
FittingC33×C9×C37C3
socleC33×C37C33
prime radicalC34×C37C32
cosocleC32×C37C34
hypercenterC33×C9C37⋊C3
hypocenterC37C3×#6887
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C32×C9 ◁ C33×C9

1052 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Conjugacy classes & character table

3213 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 3268);