Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | #382×D53 |
| Fitting | C53×#382 ⋊ C2 |
| Sylow | C53 ⋊ C2×#382 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D53 |
| commutator | C22×C53 | C23×C4 |
| Fitting | C53×#382 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | #382 | D53 |
| hypocenter | C53 | C2×#382 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #382 | |
712 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
784 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1286, #27273882, D53×#1295, … |
| maximal normal subgroup of | D53×#1286, #27273882, D53×#1295, … |
| maximal quotient of | D53×#1434, D53×C4⋊#95, #27305319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6894);