Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C23×#11719940 |
| Sylow | C53 ⋊ C23×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×#6157 |
| commutator | C2×C53 | C24×C4 |
| Frattini | C2 | C24×#6157 |
| Fitting | C25×C53 | C4 |
| socle | C24×C53 | C2×C4 |
| hypercenter | C25 | #6157 |
| hypocenter | C53 | C23×M16 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C25 | |
1720 conjugacy classes of subgroups.
496 conjugacy classes — view the full character table.
| maximal subgroup of | #28306435, #28306473, #28306503, … |
| maximal normal subgroup of | #28306435, #28306473, #28306503, … |
| maximal quotient of | C23×#13133272, C22×C4×#11719940, C23×C22⋊#88324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21495);