Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | #350×D61 |
| Fitting | C61×#350 ⋊ C2 |
| Sylow | C61 ⋊ C2×#350 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D4×D61 |
| commutator | C4×C61 | C22×C8 |
| Frattini | C2×C8 | C22×D61 |
| Fitting | C61×#350 | C2 |
| socle | C2×C61 | C2×C22⋊C8 |
| hypercenter | #350 | D61 |
| hypocenter | C61 | C2×#350 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #350 | |
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
896 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#350×D61, D61×#2117, #29832717, … |
| maximal normal subgroup of | C2×#350×D61, D61×#2117, #29832717, … |
| maximal quotient of | D61×#1315, #29589086, D61×#1323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6132);