Finite Group Databasebeta

C3×#22582457 #41005300

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

Aliases

direct productC3×#22582457

Splittings

SylowC37 ⋊ C3×#6861

Subgroups

subgroupG/H
centerC33C32⋊(C37⋊C3)
commutator, cosocleC33×C37C33
FrattiniC33C32×C37⋊C3
FittingC3×C37×C32⋊C9C3
socleC33×C37H(3,𝔽3)
prime radicalC34×C37C32
hypercenterC3×C32⋊C9C37⋊C3
hypocenterC37C3×#6861
LCSG ▷ C33×C37 ▷ C32×C37 ▷ C37
UCSC1 ◁ C33 ◁ C34 ◁ C3×C32⋊C9

284 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Conjugacy classes & character table

1293 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 1071);