Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #461×D61 |
| Fitting | C61×#461 ⋊ C2 |
| Sylow | C61 ⋊ C2×#461 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D61 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#461 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #461 | D61 |
| hypocenter | C61 | C2×#461 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #461 | |
544 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1639, D61×#1643, D61×#1647, … |
| maximal normal subgroup of | D61×#1639, D61×#1643, D61×#1647, … |
| maximal quotient of | D61×#1671, D61×#1673, D61×#1675, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13924);