Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C17 ⋊ SD16 |
| Sylow | C17 ⋊ #204 |
| Sylow | C3 ⋊ #63230 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 408 |
Polycyclic presentation:
2^4,3,17|a^2=c,b^2=d,c^2=d,b^a=bcd,f^a=f^16,c^b=cd,e^b=e^287 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#204, #13108986, #13108998, … |
| maximal normal subgroup of | D17×#204, #13108986, #13108998, … |
| maximal quotient of | #13108710, #13108714, #13108726, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 21);