Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3056 |
496 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=g,b^2=e,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,h^b=h^52760 conjugacy classes — view the full character table.
| maximal subgroup of | #27421529, #27421533, #27421551, … |
| maximal normal subgroup of | #27421529, #27421533, #27421551, … |
| maximal quotient of | #27366867, #27366889, #27366911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14136);