Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #424×D53 |
| Fitting | C53×#424 ⋊ C2 |
| Sylow | C53 ⋊ C2×#424 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D53 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C53×#424 | C2 |
| hypercenter | #424 | D53 |
| hypocenter | C53 | C2×#424 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #424 | |
512 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1323, #27293234, #27293237, … |
| maximal normal subgroup of | D53×#1323, #27293234, #27293237, … |
| maximal quotient of | D53×#1570, D53×#1571, D53×#1572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13066);