Finite Group DatabasebetaFinite Group Databasebeta| order | 7821 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C79⋊C9 |
| unambiguous semidirect product | C79⋊(C9×C11) |
| unambiguous semidirect product | (C11×C79)⋊C9 |
| derived, Sylow | C79 ⋊ C9×C11 |
| Hall | C11×C79 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | C79⋊C3 |
| commutator, hypocenter | C79 | C9×C11 |
| Frattini | C3 | C11×C79⋊C3 |
| Fitting, socle | C3×C11×C79 | C3 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C3×C11 | |
12 conjugacy classes of subgroups.
957 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C11×C79⋊C9, C11×D79⋊C9, D11×C79⋊C9, … |
| maximal normal subgroup of | C2×C11×C79⋊C9, C11×D79⋊C9, D11×C79⋊C9, … |
| maximal quotient of | C2×C11×C79⋊C9, C11×C22⋊(C79⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7821, 2);