Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42 |
| direct product | C2×#16840698 |
| unambiguous semidirect product | D61⋊#376 |
| Fitting | C2×C42×C61 ⋊ C4 |
| Sylow | C61 ⋊ C2×#376 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#6923 |
| commutator | C2×C61 | C22×C42 |
| Frattini | C22 | C23×#6923 |
| Fitting | C2×C42×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C2×C42 | #6923 |
| hypocenter | C61 | C2×#376 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
840 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 338 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
560 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21460642, #30596003, #30596010, … |
| maximal normal subgroup of | C2×#21460642, #30596003, #30596010, … |
| maximal quotient of | C2×C4×(C2×#6923)⋊C4, C4×#16840698, C2×#21460994, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20937);