Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#22575486 |
| Fitting | C2×M16×C269 ⋊ C2 |
| Sylow | C269 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8608 |
2702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46811253, #46811255, #46811357, … |
| maximal normal subgroup of | #46811253, #46811255, #46811357, … |
| maximal quotient of | C2×#31770615, C2×#31770607, C2×#31770647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1344);