Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
| direct product | #97×#6157 |
| Fitting | #97×C53 ⋊ C4 |
| Sylow | C53 ⋊ C4×#97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6157 |
| commutator | C2×C53 | C43 |
| Fitting | #97×C53 | C4 |
| socle | C22×C53 | C2×C42 |
| hypercenter | #97 | #6157 |
| hypocenter | C53 | C4×#97 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
360 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
340 conjugacy classes — view the full character table.
| maximal subgroup of | #329×#6157, #330×#6157, #28301870, … |
| maximal normal subgroup of | #329×#6157, #330×#6157, #28301870, … |
| maximal quotient of | #322×#6157, #97×#88324, #28300035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20163);