Finite Group Databasebeta

#737×#66524 #41007513

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

Aliases

direct product#737×#66524

Splittings

SylowC37 ⋊ C9×#737

Subgroups

subgroupG/H
centerC3×C9C32×C37⋊C3
commutatorC3×C37C33×C9
FrattiniC32C33×C37⋊C3
FittingC3×C37×#737C3
socle, cosocleC32×C37C34
prime radicalC3×H(3,𝔽3)×C37C32
hypercenterC3×#737C37⋊C3
hypocenterC37C9×#737
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C3×C9 ◁ C3×#737

986 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, 3284);