Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q8×C22⋊D269 |
| Fitting | C22×Q8×C269 ⋊ C2 |
| Sylow | C269 ⋊ D4×Q8 |
280 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8608 |
2705 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46822388, #46822389, #46822395, … |
| maximal normal subgroup of | #46822388, #46822389, #46822395, … |
| maximal quotient of | Q8×#16864379, Q8×C22⋊Dic269, C4⋊C4×C22⋊D269, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1213);