Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | (C2×#11761640)⋊Q8 |
| Fitting | C2×Q8×C269 ⋊ C4 |
| Sylow | C269 ⋊ #391 |
186 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 64 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=f,b^2=def,c^2=e,b^a=bd,c^a=ce,g^a=g^82,g^b=g^187,g^f=g^268698 conjugacy classes — view the full character table.
| maximal subgroup of | #46825981 |
| maximal normal subgroup of | #46825981 |
| maximal quotient of | #46826062, #46826064, #46826070, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1502);