Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #443×D53 |
| Fitting | C53×#443 ⋊ C2 |
| Sylow | C53 ⋊ C2×#443 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D4×D53 |
| commutator | C4×C53 | C23×C4 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#443 | C2 |
| socle | C2×C53 | C2×C4×D4 |
| hypercenter | #443 | D53 |
| hypocenter | C53 | C2×#443 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #443 | |
472 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1335, #27293877, D53×#1336, … |
| maximal normal subgroup of | D53×#1335, #27293877, D53×#1336, … |
| maximal quotient of | C8×D8×D53, C8×SD16×D53, C8×Q16×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13396);