Finite Group Databasebeta

C3×#22582492 #41006329

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

Aliases

direct productC3×#22582492

Splittings

SylowC37 ⋊ C3×#6875

Subgroups

subgroupG/H
centerC32#15688505
commutatorC9×C37C32×C9
FrattiniC3×C9C32×C37⋊C3
FittingC3×C37×C27⋊C3C3
socleC32×C37C9⋊C9
prime radicalC33×C373−1+2
cosocleC3×C9×C37C33
hypercenterC3×C27⋊C3C37⋊C3
hypocenterC37C3×#6875
LCSG ▷ C9×C37 ▷ C3×C37 ▷ C37
UCSC1 ◁ C32 ◁ C32×C9 ◁ C3×C27⋊C3

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2997

Conjugacy classes & character table

1293 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 2100);