Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #578×D61 |
| Fitting | C61×#578 ⋊ C2 |
| Sylow | C61 ⋊ C2×#578 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D4×D61 |
| commutator | C4×C61 | C25 |
| Frattini | C4 | C24×D61 |
| Fitting | C61×#578 | C2 |
| socle | C2×C61 | C23×D4 |
| hypercenter | #578 | D61 |
| hypocenter | C61 | C2×#578 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #578 | |
1408 conjugacy classes of subgroups.
704 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#2193, D61×#2195, #29833984, … |
| maximal normal subgroup of | D61×#2193, D61×#2195, #29833984, … |
| maximal quotient of | D61×#2898, D61×#2913, D61×#2947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19272);