Finite Group Databasebeta

C37⋊C3×#6879 #41007325

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

Aliases

direct productC37⋊C3×#6879

Splittings

FittingC37×#6879 ⋊ C3
SylowC37 ⋊ C3×#6879

Subgroups

subgroupG/H
centerC3#732×C37⋊C3
commutator, cosocleC3×C9×C37C33
FrattiniC3×C9C32×C37⋊C3
FittingC37×#6879C3
socleC3×C37C3×#732
hypercenter#6879C37⋊C3
hypocenterC37C3×#6879
LCSG ▷ C3×C9×C37 ▷ C32×C37 ▷ C3×C37 ▷ C37
UCSC1 ◁ C3 ◁ C32 ◁ C3×C9 ◁ #6879

260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 999

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 3096);