Finite Group DatabasebetaFinite Group Databasebeta| order | 16784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C1049 ⋊ C2 |
| Sylow | C1049 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8392 |
Polycyclic presentation:
2^4,1049|a^2=d,b^a=bc,e^b=e^10484202 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D1049, C2×#30680893, #46776908, … |
| maximal normal subgroup of | C22⋊C4×D1049, C2×#30680893, #46776908, … |
| maximal quotient of | #46776858, #46776863, #46776865, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16784, 17);