Finite Group Databasebeta

C3×C27×#66526 #41008462

order26973
automorphism?
homologyAbelianization (H1) = C3×C9×C27 · Schur multiplier (H2) = C32×C9

Aliases

direct productC3×C27×#66526

Splittings

FittingC3×C27×C37 ⋊ C9
derived, SylowC37 ⋊ C3×C9×C27

Subgroups

subgroupG/H
center, hypercenterC3×C27#66526
commutator, hypocenterC37C3×C9×C27
FrattiniC9C32×#66526
FittingC3×C27×C37C9
socleC32×C37C92
prime radicalC32×C37⋊C3C3×C9
cosocleC9×C37⋊C3C33
LCSG ▷ C37
UCSC1 ◁ C3×C27

404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2997

Conjugacy classes & character table

1053 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 4233);