Finite Group Databasebeta

C9×#15688509 #41006196

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

Aliases

direct productC9×#15688509

Splittings

FittingC9×C27×C37 ⋊ C3
SylowC37 ⋊ C9×C27⋊C3

Subgroups

subgroupG/H
centerC92C3×C37⋊C3
commutatorC3×C37C3×C92
FrattiniC3×C9C32×C37⋊C3
FittingC9×C27×C37C3
socleC32×C37C32×C9
prime radicalC32×C37⋊C3C3×C9
cosocleC3×C9×C37C33
hypercenterC9×C27C37⋊C3
hypocenterC37C9×C27⋊C3
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C92 ◁ C9×C27

320 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, 1967);