Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #473×D61 |
| Fitting | C61×#473 ⋊ C2 |
| Sylow | C61 ⋊ C2×#473 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #121×D61 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#473 | C2 |
| socle | C2×C61 | C2×#121 |
| hypercenter | #473 | D61 |
| hypocenter | C61 | C2×#473 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #473 | |
448 conjugacy classes of subgroups.
512 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#2194, D61×#2195, #29834002, … |
| maximal normal subgroup of | D61×#2194, D61×#2195, #29834002, … |
| maximal quotient of | D61×#1669, D61×#1673, D61×#1679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 14219);