Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D269⋊M32 |
| Sylow | C269 ⋊ C2×M32 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|a^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^187,g^c=g^268,g^d=g^2681112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46825928, #46825931, #46825934, … |
| maximal normal subgroup of | #46825928, #46825931, #46825934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1605);