Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#16810814 |
| Fitting | C2×#99×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#458 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13133187 |
| commutator | C23×C53 | C24 |
| Frattini | C23 | C23×D53 |
| Fitting | C2×#99×C53 | C2 |
| socle | C22×C53 | #120 |
| hypercenter | C2×#99 | D53 |
| hypocenter | C53 | C2×#458 |
| LCS | G ▷ C23×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C2×#99 | |
794 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
604 conjugacy classes — view the full character table.
| maximal subgroup of | #27301358, #27301360, #27301372, … |
| maximal normal subgroup of | #27301358, #27301360, #27301372, … |
| maximal quotient of | C2×#20273702, C2×#20273703, C2×#20273736, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13899);