Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#131×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2897 |
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|a^2=f,e^2=g,b^a=be,e^a=eg,h^a=h^52,e^b=eg,h^b=h^52,d^c=dg1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27400068, #27400072, #27400079, … |
| maximal normal subgroup of | #27400068, #27400072, #27400079, … |
| maximal quotient of | #27350475, #27350571, #27350672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13037);