Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | #353×D53 |
| Fitting | C53×#353 ⋊ C2 |
| Sylow | C53 ⋊ C2×#353 |
368 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
364 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1402, #27304313, D53×#1408, … |
| maximal normal subgroup of | D53×#1402, #27304313, D53×#1408, … |
| maximal quotient of | D53×#1318, D53×#1325, #27293359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6166);