Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×#16811258 |
| Fitting | C2×#127×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×D42 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D53 |
| commutator | C22×C53 | C25 |
| Frattini | C22 | C24×D53 |
| Fitting | C2×#127×C53 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | C2×#127 | D53 |
| hypocenter | C53 | C2×D42 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
2536 conjugacy classes of subgroups; only the 581 normal subgroups are shown.
This group has 2536 conjugacy classes of subgroups — too many to draw. Only its 581 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
778 conjugacy classes — view the full character table.
| maximal subgroup of | #27275792, #27276156, #27276160, … |
| maximal normal subgroup of | #27275792, #27276156, #27276160, … |
| maximal quotient of | C2×#20277536, C2×#20277615, C2×#20277696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17949);