Finite Group Databasebeta

C32×#15688530 #41008249

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

Aliases

direct productC32×#15688530

Splittings

SylowC37 ⋊ C32×#737

Subgroups

subgroupG/H
centerC33C32×C37⋊C3
commutator, cosocleC3×C37C35
FrattiniC3C34×C37⋊C3
Fitting, prime radicalC32×H(3,𝔽3)×C37C3
socleC33×C37C33
hypercenterC32×H(3,𝔽3)C37⋊C3
hypocenterC37C32×#737
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C33 ◁ C32×H(3,𝔽3)

5804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Conjugacy classes & character table

1485 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 4020);