Finite Group Databasebeta

C33×#11758608 #41008247

order26973
automorphism?
homologyAbelianization (H1) = C35 · Schur multiplier (H2) = C39

Aliases

direct productC33×#11758608

Splittings

SylowC37 ⋊ C33×3−1+2

Subgroups

subgroupG/H
centerC34C3×C37⋊C3
commutator, cosocleC3×C37C35
FrattiniC3C34×C37⋊C3
Fitting, prime radicalC35×C37C3
socleC34×C37C32
hypercenterC35C37⋊C3
hypocenterC37C33×3−1+2
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C34 ◁ C35

7208 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, 4018);