Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q16×Dic269 |
| Sylow | C269 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
1904 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46812734, SD32×Dic269, #46812741, … |
| maximal normal subgroup of | #46812734, SD32×Dic269, #46812741, … |
| maximal quotient of | Q16×#14524130, #46809736, #46809782, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 644);