Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×Dic12 |
| Hall | C3×C17 ⋊ Q16 |
| Sylow | C3 ⋊ Q16×C17 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 816 |
255 conjugacy classes — view the full character table.
| maximal subgroup of | #13108681, #13108686, #13108687, … |
| maximal normal subgroup of | #13108681, #13108686, #13108687, … |
| maximal quotient of | C17×#818, C17×#816, C2×C17×Dic12 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 53);