Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #441×D53 |
| Fitting | C53×#441 ⋊ C2 |
| Sylow | C53 ⋊ C2×#441 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D53 |
| commutator | C4×C53 | C23×C4 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#441 | C2 |
| socle | C22×C53 | C22×D4 |
| hypercenter | #441 | D53 |
| hypocenter | C53 | C2×#441 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #441 | |
480 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
616 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2180, C2×#441×D53, D53×#2943, … |
| maximal normal subgroup of | D53×#2180, C2×#441×D53, D53×#2943, … |
| maximal quotient of | D53×#1579, D53×#1587, D53×#1593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13293);