Finite Group Databasebeta

C37⋊C3×#6894 #41007558

order26973
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C34

Aliases

direct productC37⋊C3×#6894

Splittings

FittingC37×#6894 ⋊ C3
SylowC37 ⋊ C3×#6894

Subgroups

subgroupG/H
center, FrattiniC32C33×C37⋊C3
commutator, socle, cosocleC32×C37C34
FittingC37×#6894C3
prime radicalC33×C37⋊C3C32
hypercenter#6894C37⋊C3
hypocenterC37C3×#6894
LCSG ▷ C32×C37 ▷ C37
UCSC1 ◁ C32 ◁ #6894

932 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2997

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 3329);