Finite Group Databasebeta

C33×#11758605 #41008246

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

Aliases

direct productC33×#11758605

Splittings

FittingC33×C9×C37 ⋊ C3
SylowC37 ⋊ C33×3−1+2

Subgroups

subgroupG/H
centerC34C3×C37⋊C3
commutator, cosocleC3×C37C35
FrattiniC3C34×C37⋊C3
FittingC33×C9×C37C3
socleC34×C37C32
prime radicalC34×C37⋊C3C3
hypercenterC33×C9C37⋊C3
hypocenterC37C33×3−1+2
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C34 ◁ C33×C9

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, 4017);