Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C17 ⋊ M16 |
| Sylow | C17 ⋊ #208 |
| Sylow | C3 ⋊ #63243 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 408 |
Polycyclic presentation:
2^4,3,17|a^2=c,b^2=d,c^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 | #13108892, #13108893, #13108898, … |
| maximal normal subgroup of | #13108892, #13108893, #13108898, … |
| maximal quotient of | #13108967, #13108968, C4⋊(C3⋊#3624), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 115);