Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C81 · Schur multiplier (H2) = C9 |
No aliases for this group.
| derived, Sylow | C37 ⋊ C9×C81 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C27 | #66526 |
| commutator, hypocenter | C37 | C9×C81 |
| Frattini | C3×C9 | C3×#66526 |
| Fitting | C3×C27×C37 | C9 |
| socle, prime radical | C32×C37 | C3×C27 |
| cosocle | C3×#11758601 | C32 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3×C27 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26973 |
Polycyclic presentation:
3^6,37|a^3=c,b^3=d,c^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, 4114);