Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C269 ⋊ #462 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
Polycyclic presentation:
2^6,269|a^2=f,b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^268,e^c=ef,g^c=g^2682699 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46810072, #46810074, #46810079, … |
| maximal normal subgroup of | #46810072, #46810074, #46810079, … |
| maximal quotient of | #46810268, #46810280, #46810290, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 760);