Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#22575365 |
| Fitting | C22×C8×C269 ⋊ C2 |
| Sylow | C269 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 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 | #46808808, #46810642, C4×#22575365, … |
| maximal normal subgroup of | #46808808, #46810642, C4×#22575365, … |
| maximal quotient of | C2×#31770328, C2×#31770330, #46809197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 509);