Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | #389×D53 |
| Fitting | C53×#389 ⋊ C2 |
| Sylow | C53 ⋊ C2×#389 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D53 |
| commutator | C22×C53 | C23×C4 |
| Fitting | C53×#389 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | #389 | D53 |
| hypocenter | C53 | C2×#389 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #389 | |
800 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1271, #27272079, #27272092, … |
| maximal normal subgroup of | D53×#1271, #27272079, #27272092, … |
| maximal quotient of | D53×C4⋊#95, D53×#1436, #27305282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6957);