Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #508×D53 |
| Fitting | C53×#508 ⋊ C2 |
| Sylow | C53 ⋊ C2×#508 |
368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
616 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1417, #27304545, D53×#1418, … |
| maximal normal subgroup of | D53×#1417, #27304545, D53×#1418, … |
| maximal quotient of | D53×#2138, D53×#2158, C4×D16×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17624);