Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#16810677 |
| Sylow | C53 ⋊ C2×#432 |
488 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1096 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27273693, #27273699, #27273706, … |
| maximal normal subgroup of | #27273693, #27273699, #27273706, … |
| maximal quotient of | C2×#20274462, C2×#20274479, C2×#20274567, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13128);