Finite Group Databasebeta

C3×(C37⋊C3)⋊C81 #41008625

order26973
automorphism?
homologyAbelianization (H1) = C32×C81 · Schur multiplier (H2) = C33

Aliases

direct productC3×(C37⋊C3)⋊C81
unambiguous semidirect product(C37⋊C3)⋊(C3×C81)

Splittings

derived, SylowC37 ⋊ C32×C81

Subgroups

subgroupG/H
center, hypercenterC3×C27#66526
commutator, hypocenterC37C32×C81
FrattiniC9C32×#66526
FittingC3×C27×C37C9
socleC32×C37C3×C27
prime radicalC32×C37⋊C3C27
cosocle#11758601C33
LCSG ▷ C37
UCSC1 ◁ C3×C27

188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

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, 4396);