Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C3⋊#595) |
| Fitting | C3×C4×C17 ⋊ C4 |
| Hall | C3×C17 ⋊ C4⋊C4 |
| Sylow | C17 ⋊ C4⋊Dic3 |
| Sylow | C3 ⋊ C4⋊#595 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 204 |
Polycyclic presentation:
2^4,3,17|a^2=c,b^2=d,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 | #13108889, #13108891, #13108896, … |
| maximal normal subgroup of | #13108889, #13108891, #13108896, … |
| maximal quotient of | #13108959, #13108960, #13108961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 117);