Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C8×#6157 |
| Fitting | C22×C8×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C22×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | #6157 |
| commutator, hypocenter | C53 | C22×C4×C8 |
| Frattini | C4 | C23×#6157 |
| Fitting | C22×C8×C53 | C4 |
| socle | C23×C53 | C42 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22×C8 | |
760 conjugacy classes of subgroups; only the 418 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 418 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
544 conjugacy classes — view the full character table.
| maximal subgroup of | #336×#6157, #28306350, #28306354, … |
| maximal normal subgroup of | #336×#6157, #28306350, #28306354, … |
| maximal quotient of | C22×C8×#88324, C2×C8×D53⋊C8, C22×#88324⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21058);