Finite Group DatabasebetaFinite Group Databasebeta| order | 26487 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C81 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived, Sylow | C109 ⋊ C3×C81 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #15668887 |
| commutator, hypocenter | C109 | C3×C81 |
| Frattini | C3 | C3×#15668887 |
| Fitting | C9×C109 | C27 |
| socle | C3×C109 | C3×C27 |
| prime radical | C3×C109⋊C3 | C27 |
| cosocle | #15668885 | C32 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C9 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8829 |
Polycyclic presentation:
3^5,109|a^3=c,c^3=d,d^3=e,f^a=f^97,f^b=f^45,f^c=f^16,f^d=f^63279 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26487, 368);