Finite Group Databasebeta

C37⋊C3×#6864 #41006192

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

Aliases

direct productC37⋊C3×#6864

Splittings

FittingC37×#6864 ⋊ C3
SylowC37 ⋊ C3×#6864

Subgroups

subgroupG/H
center, FrattiniC3×C9C32×C37⋊C3
commutatorC3×C37C3×C92
FittingC37×#6864C3
socleC32×C37C32×C9
prime radicalC32×C37⋊C3C3×C9
cosocleC3×C9×C37C33
hypercenter#6864C37⋊C3
hypocenterC37C3×#6864
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C3×C9 ◁ #6864

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Conjugacy classes & character table

1485 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 1963);