Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C8×C22⋊D269 |
| Fitting | C22×C8×C269 ⋊ C2 |
| Sylow | C269 ⋊ C8×D4 |
134 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8608 |
4328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46812702, C16×C22⋊D269, #46812707, … |
| maximal normal subgroup of | #46812702, C16×C22⋊D269, #46812707, … |
| maximal quotient of | C8×#16864387, C8×#16864390, C8×#16864389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 613);