Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C17 ⋊ Q16 |
| Sylow | C17 ⋊ #216 |
| Sylow | C3 ⋊ #63231 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 816 |
Polycyclic presentation:
2^4,3,17|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^16,c^b=cd132 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#216, #13109245, D3×#63231, … |
| maximal normal subgroup of | D17×#216, #13109245, D3×#63231, … |
| maximal quotient of | #13108832, #13108835, #13108860, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 79);