Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#16864390 |
| Sylow | C269 ⋊ C4×SD16 |
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8608 |
2708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#16864390, #46809688, #46809694, … |
| maximal normal subgroup of | C8×#16864390, #46809688, #46809694, … |
| maximal quotient of | C8×#16864390, #46809721, #46809726, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 635);