Finite Group Databasebeta

C9×#15688505 #41005093

order26973
automorphism?
homologyAbelianization (H1) = C3×C92 · Schur multiplier (H2) = C32×C9

Aliases

direct productC9×#15688505

Splittings

SylowC37 ⋊ C9×C9⋊C9

Subgroups

subgroupG/H
centerC32×C9C3×C37⋊C3
commutatorC3×C37C3×C92
FrattiniC33C32×C37⋊C3
FittingC3×C92×C37C3
socle, prime radical, cosocleC33×C37C33
hypercenterC3×C92C37⋊C3
hypocenterC37C9×C9⋊C9
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C32×C9 ◁ C3×C92

482 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, 864);