Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #100×D269 |
| Fitting | #100×C269 ⋊ C2 |
| Sylow | C269 ⋊ C2×#100 |
186 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2152 |
1496 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AΣL(1,𝔽16)×D269, #352×D269, #46812528, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D269, #352×D269, #46812528, … |
| maximal quotient of | #323×D269, #46809204, #46809210, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 524);