Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic66⋊C5 |
| Hall | Dic66 ⋊ C5 |
| Hall | C3×C11⋊C5 ⋊ Q8 |
| Hall | C11⋊C5 ⋊ Dic6 |
| Hall | C3×C11 ⋊ C5×Q8 |
| Sylow | C11 ⋊ C5×Dic6 |
| Sylow | C3 ⋊ (C11⋊C5)⋊Q8 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^2,5,2,3,11|a^2=d,b^2=d,b^a=bd,e^a=e^2,f^a=f^10,f^c=f^557 conjugacy classes — view the full character table.
| maximal subgroup of | #72216791, #72216807, #72216818, … |
| maximal normal subgroup of | #72216791, #72216807, #72216818, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 33);