Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | #504×D53 |
| Fitting | C53×#504 ⋊ C2 |
| Sylow | C53 ⋊ C2×#504 |
| subgroup | G/H | |
|---|---|---|
| center | C16 | C22×D53 |
| commutator, socle | C2×C53 | C23×C8 |
| Frattini | C8 | C23×D53 |
| Fitting | C53×#504 | C2 |
| hypercenter | #504 | D53 |
| hypocenter | C53 | C2×#504 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C16 ◁ #504 | |
368 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 211 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1401, #27304301, D53×#2170, … |
| maximal normal subgroup of | D53×#1401, #27304301, D53×#2170, … |
| maximal quotient of | D53×#2108, #504×Dic53, #27536736, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17607);