Finite Group Databasebeta

C3×C32⋊#11758601 #41006209

order26973
automorphism?
homologyAbelianization (H1) = C32×C27 · Schur multiplier (H2) = C34

Aliases

direct productC3×C32⋊#11758601

Splittings

SylowC37 ⋊ C3×C32⋊C27

Subgroups

subgroupG/H
centerC32×C9C3×C37⋊C3
commutatorC3×C37C32×C27
FrattiniC3×C9C32×C37⋊C3
FittingC33×C9×C37C3
socleC33×C37C3×C9
prime radicalC34×C37C9
cosocleC3×C9×C37C33
hypercenterC33×C9C37⋊C3
hypocenterC37C3×C32⋊C27
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C32×C9 ◁ C33×C9

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Conjugacy classes & character table

3213 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 1980);