Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×C3×C17 ⋊ C4 |
| Hall | C3×C17 ⋊ C22⋊C4 |
| Sylow | C17 ⋊ #217 |
| Sylow | C3 ⋊ C22⋊#595 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 204 |
Polycyclic presentation:
2^4,3,17|a^2=c,b^a=bd,e^a=e^2,f^a=f^4,f^c=f^1666 conjugacy classes — view the full character table.
| maximal subgroup of | #13108909, #13108910, #13108965, … |
| maximal normal subgroup of | #13108909, #13108910, #13108965, … |
| maximal quotient of | #13108965, #13108968, #13108971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 120);