Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D269⋊(C22⋊C8) |
| Sylow | C269 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|a^2=e,e^2=f,b^a=bd,g^a=g^187,g^c=g^268,g^e=g^2681112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46825722, #46825727, #46825747, … |
| maximal normal subgroup of | #46825722, #46825727, #46825747, … |
| maximal quotient of | #46826111, #46826114, #46826117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1517);