Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#16864392 |
| Sylow | C269 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
2708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46809689, C8×#16864392, #46809701, … |
| maximal normal subgroup of | #46809689, C8×#16864392, #46809701, … |
| maximal quotient of | C8×#16864392, #46809733, #46809735, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 642);