Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×H(5,𝔽2)×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3008 |
784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^52,e^b=eg,d^c=dg916 conjugacy classes — view the full character table.
| maximal subgroup of | #27301670, #27301672, #27301691, … |
| maximal normal subgroup of | #27301670, #27301672, #27301691, … |
| maximal quotient of | #27357254, #27357342, #27357428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13778);