Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#13133240 |
| Fitting | C22×Q16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22×#135 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D53 |
| commutator | C4×C53 | C25 |
| Frattini | C4 | C24×D53 |
| Fitting | C22×Q16×C53 | C2 |
| socle | C23×C53 | C2×D4 |
| hypercenter | C22×Q16 | D53 |
| hypocenter | C53 | C22×#135 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×Q16 | |
1504 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 525 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 | #27299742, #27299763, #27385438, … |
| maximal normal subgroup of | #27299742, #27299763, #27385438, … |
| maximal quotient of | C22×#16810618, C22×#16810660, C22×#16810705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19239);