Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#117×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3093 |
414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|b^2=g,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^52,f^c=fg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27416906, #27416909, #27416914, … |
| maximal normal subgroup of | #27416906, #27416909, #27416914, … |
| maximal quotient of | #27383896, #27384832, #27385327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14441);