Finite Group Databasebeta

C3×#22582462 #41006193

order26973
automorphism?
homologyAbelianization (H1) = C3×C92 · Schur multiplier (H2) = C33

Aliases

direct productC3×#22582462

Splittings

SylowC37 ⋊ C3×#6864

Subgroups

subgroupG/H
centerC32×C9C3×C37⋊C3
commutatorC3×C37C3×C92
FrattiniC3×C9C32×C37⋊C3
FittingC32×C27×C37C3
socle, prime radicalC33×C37C3×C9
cosocleC3×C9×C37C33
hypercenterC32×C27C37⋊C3
hypocenterC37C3×#6864
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C32×C9 ◁ C32×C27

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26973

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, 1964);