Finite Group Databasebeta

C3×#22582731 #41008650

order26973
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C35

Aliases

direct productC3×#22582731

Splittings

SylowC37 ⋊ C3×#6903

Subgroups

subgroupG/H
centerC32C32×#66526
commutatorC3×C37C33×C9
FrattiniC3C33×#66526
Fitting, prime radicalC3×H(3,𝔽3)×C37C9
socleC32×C37C32×C9
cosocle#66524C34
hypercenterC3×H(3,𝔽3)#66526
hypocenterC37C3×#6903
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C32 ◁ C3×H(3,𝔽3)

848 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 4421);