Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#22575451 |
| Sylow | C269 ⋊ C2×C4⋊Q8 |
290 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
2708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46811275, #46811276, #46811278, … |
| maximal normal subgroup of | #46811275, #46811276, #46811278, … |
| maximal quotient of | C2×#31770474, C2×#31770500, C2×#31770510, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1091);