Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #564×D61 |
| Fitting | C61×#564 ⋊ C2 |
| Sylow | C61 ⋊ C2×#564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D61 |
| commutator, socle | C22×C61 | C25 |
| Fitting | C61×#564 | C2 |
| hypercenter | #564 | D61 |
| hypocenter | C61 | C2×#564 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #564 | |
896 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1658, D61×#1663, #29661313, … |
| maximal normal subgroup of | D61×#1658, D61×#1663, #29661313, … |
| maximal quotient of | D61×#2382, #29842733, #564×Dic61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 18652);