Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C243 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C37⋊C3)⋊C243 |
| derived, Sylow | C37 ⋊ C3×C243 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C81 | #66526 |
| commutator, hypocenter | C37 | C3×C243 |
| Frattini | C27 | C3×#66526 |
| Fitting | C37×C81 | C9 |
| socle | C3×C37 | C3×C81 |
| prime radical | C3×C37⋊C3 | C81 |
| cosocle | #15688500 | C32 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C81 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8991 |
Polycyclic presentation:
3^6,37|a^3=c,c^3=d,d^3=e,e^3=f,g^a=g^16,g^b=g^10,g^c=g^261053 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 4200);