Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | #127×#6923 |
| Fitting | #127×C61 ⋊ C4 |
| Sylow | C61 ⋊ C4×#127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | #127×C61 | C4 |
| hypercenter | #127 | #6923 |
| hypocenter | C61 | C4×#127 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #127 | |
924 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
266 conjugacy classes — view the full character table.
| maximal subgroup of | #331×#6923, #30597808, #30597817, … |
| maximal normal subgroup of | #331×#6923, #30597808, #30597817, … |
| maximal quotient of | #390×#6923, #384×#6923, #392×#6923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20980);