Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×#13133139 |
| Fitting | C2×C4×C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C4×#102 |
396 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27274853, C8×#13133139, #27274867, … |
| maximal normal subgroup of | #27274853, C8×#13133139, #27274867, … |
| maximal quotient of | C4×#16810352, #27274715, #27274730, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4326);