Finite Group Databasebeta

C32×#15688509 #41008116

order26973
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C35

Aliases

direct productC32×#15688509

Splittings

FittingC32×C27×C37 ⋊ C3
SylowC37 ⋊ C32×C27⋊C3

Subgroups

subgroupG/H
centerC32×C9C3×C37⋊C3
commutatorC3×C37C33×C9
FrattiniC9C33×C37⋊C3
FittingC32×C27×C37C3
socleC33×C37C3×C9
prime radicalC33×C37⋊C3C9
cosocleC9×C37C34
hypercenterC32×C27C37⋊C3
hypocenterC37C32×C27⋊C3
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C32×C9 ◁ C32×C27

944 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, 3887);