Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#2117 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C53 | C2×D4 |
| commutator | C4 | C22×C8×C53 |
| Frattini, cosocle | C2×C8 | C23×C53 |
| socle | C2×C53 | C2×C22⋊C8 |
| prime radical | C2×#41×C53 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C53 ◁ C22×C8×C53 ◁ G | |
220 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2332 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 849);