Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | #458×D53 |
| Fitting | C53×#458 ⋊ C2 |
| Sylow | C53 ⋊ C2×#458 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #120×D53 |
| commutator | C23×C53 | C24 |
| Frattini | C23 | C23×D53 |
| Fitting | C53×#458 | C2 |
| socle | C2×C53 | C2×#120 |
| hypercenter | #458 | D53 |
| hypocenter | C53 | C2×#458 |
| LCS | G ▷ C23×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #458 | |
794 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
448 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2197, D53×#2198, D53×#2200, … |
| maximal normal subgroup of | D53×#2197, D53×#2198, D53×#2200, … |
| maximal quotient of | D53×#1607, D53×#1613, D53×#1608, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13896);