Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#22575511 |
| Fitting | C24×C269 ⋊ C4 |
| Sylow | C269 ⋊ C2×#99 |
210 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4304 |
1094 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46825969, #46825970 |
| maximal normal subgroup of | #46825969, #46825970 |
| maximal quotient of | C2×#31771448, C2×#31771451, #46826120 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1525);