Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#16811276 |
| Fitting | C2×C4⋊Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#547 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D53 |
| commutator | C22×C53 | C25 |
| Frattini | C22 | C24×D53 |
| Fitting | C2×C4⋊Q8×C53 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | C2×C4⋊Q8 | D53 |
| hypocenter | C53 | C2×#547 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊Q8 | |
1632 conjugacy classes of subgroups.
778 conjugacy classes — view the full character table.
| maximal subgroup of | #27275812, #27275842, #27276173, … |
| maximal normal subgroup of | #27275812, #27275842, #27276173, … |
| maximal quotient of | C2×#20277544, C2×#20277583, C2×#20277615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17969);