Finite Group DatabasebetaFinite Group Databasebeta| order | 7761 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C199⋊C3 |
| unambiguous semidirect product | C199⋊(C3×C13) |
| Fitting, socle, Hall | C13×C199 ⋊ C3 |
| derived, Sylow | C199 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C199⋊C3 |
| commutator, hypocenter | C199 | C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C199 | C3 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C13 | |
8 conjugacy classes of subgroups.
897 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C13×C199⋊C3, C13×D199⋊C3, D13×C199⋊C3, … |
| maximal normal subgroup of | C2×C13×C199⋊C3, C13×D199⋊C3, D13×C199⋊C3, … |
| maximal quotient of | C2×C13×C199⋊C3, C13×#13184224, C3×C13×C199⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7761, 2);