Finite Group DatabasebetaFinite Group Databasebeta| order | 26757 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C991 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | C991⋊C3 |
| commutator, hypocenter | C991 | C27 |
| Fitting, cosocle | C9×C991 | C3 |
| socle, prime radical | C3×C991 | C9 |
| LCS | G ▷ C991 | |
| UCS | C1 ◁ C9 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26757 |
Polycyclic presentation:
3^3,991|a^3=b,b^3=c,d^a=d^1132997 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26757, 6);