Finite Group Databasebeta

C32×#15688506 #41007492

order26973
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C36

Aliases

direct productC32×#15688506

Splittings

SylowC37 ⋊ C32×C9⋊C9

Subgroups

subgroupG/H
centerC34C3×C37⋊C3
commutatorC3×C37C33×C9
FrattiniC32C33×C37⋊C3
FittingC33×C9×C37C3
socle, prime radicalC34×C37C32
cosocleC32×C37C34
hypercenterC33×C9C37⋊C3
hypocenterC37C32×C9⋊C9
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C34 ◁ C33×C9

1484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26973

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, 3263);