Finite Group Databasebeta

C9×#15688543 #41008472

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

Aliases

direct productC9×#15688543

Splittings

SylowC37 ⋊ C9×C27⋊C3

Subgroups

subgroupG/H
centerC3×C9C3×#66526
commutatorC3×C37C3×C92
FrattiniC32C32×#66526
FittingC92×C37C9
socleC32×C37C32×C9
prime radicalC32×C37⋊C3C3×C9
cosocleC3×#66524C33
hypercenterC92#66526
hypocenterC37C9×C27⋊C3
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C3×C9 ◁ C92

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 4243);