Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #123×#6157 |
| Fitting | #123×C53 ⋊ C4 |
| Sylow | C53 ⋊ C4×#123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6157 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | #123×C53 | C4 |
| hypercenter | #123 | #6157 |
| hypocenter | C53 | C4×#123 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ #123 | |
688 conjugacy classes of subgroups.
238 conjugacy classes — view the full character table.
| maximal subgroup of | #352×#6157, #458×#6157, C2×#123×#6157, … |
| maximal normal subgroup of | #352×#6157, #458×#6157, C2×#123×#6157, … |
| maximal quotient of | #386×#6157, #388×#6157, #385×#6157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20975);