Finite Group DatabasebetaFinite Group Databasebeta| order | 26487 |
| automorphism | ? |
| homology | Abelianization (H1) = C243 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C109 ⋊ C243 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | #15668887 |
| commutator, hypocenter | C109 | C243 |
| Fitting | C9×C109 | C27 |
| socle, prime radical | C3×C109 | C81 |
| cosocle | #22579518 | C3 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26487 |
Polycyclic presentation:
3^5,109|a^3=b,b^3=c,c^3=d,d^3=e,f^a=f^97,f^b=f^16,f^c=f^63279 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26487, 362);