Finite Group DatabasebetaFinite Group Databasebeta| order | 16784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q8×C1049 ⋊ C2 |
| Sylow | C1049 ⋊ SD16 |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8392 |
Polycyclic presentation:
2^4,1049|a^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^10482627 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D1049, C2×#30680903, #46776971, … |
| maximal normal subgroup of | SD16×D1049, C2×#30680903, #46776971, … |
| maximal quotient of | #46776871, #46776875, #46776882, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16784, 27);