Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#16864377 |
| Sylow | C269 ⋊ C22⋊C16 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=d,d^2=e,e^2=f,b^a=bc,g^a=g^2684328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46808808, #46808809, #46808810, … |
| maximal normal subgroup of | #46808808, #46808809, #46808810, … |
| maximal quotient of | #46808809, #46808825, #46808840, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 329);