Finite Group Databasebeta

C27⋊C3×#66524 #41006198

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

Aliases

direct productC27⋊C3×#66524

Splittings

SylowC37 ⋊ C9×C27⋊C3

Subgroups

subgroupG/H
center, FrattiniC3×C9C32×C37⋊C3
commutatorC3×C37C3×C92
FittingC3×C37×C27⋊C3C3
socleC32×C37C32×C9
prime radicalC33×C37C3×C9
cosocleC3×C9×C37C33
hypercenterC3×C27⋊C3C37⋊C3
hypocenterC37C9×C27⋊C3
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C3×C9 ◁ C3×C27⋊C3

320 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, 1969);