Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#16810670 |
| Fitting | C2×#108×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#430 |
460 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 460 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.
772 conjugacy classes — view the full character table.
| maximal subgroup of | #27300418, #27300421, #27300423, … |
| maximal normal subgroup of | #27300418, #27300421, #27300423, … |
| maximal quotient of | C2×#20273464, C2×#20273466, #27353074, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13115);