Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C4×C8×#6157 |
| Fitting | C4×C8×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | #6157 |
| commutator, hypocenter | C53 | C42×C8 |
| Frattini | C2×C4 | C22×#6157 |
| Fitting | C4×C8×C53 | C4 |
| socle | C22×C53 | C2×C42 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C4×C8 | |
408 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 226 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 | #28298289, C82×#6157, #322×#6157, … |
| maximal normal subgroup of | #28298289, C82×#6157, #322×#6157, … |
| maximal quotient of | C82×#6157, C4×C8×#88324, #322×#6157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20161);