Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C9⋊C8 |
| unambiguous semidirect product | C9⋊(C8×C11) |
| derived, Sylow | C9 ⋊ C8×C11 |
| Hall | C9×C11 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C11 | D9 |
| commutator, hypocenter | C9 | C8×C11 |
| Frattini | C3×C4 | D3×C11 |
| Fitting | C4×C9×C11 | C2 |
| socle, prime radical | C2×C3×C11 | Dic3 |
| cosocle | C4×C9 | C2×C11 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C4×C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 792 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D99⋊C8, #13096844, D11×C9⋊C8, … |
| maximal normal subgroup of | D99⋊C8, #13096844, D11×C9⋊C8, … |
| maximal quotient of | C11×C9⋊C16, C2×C11×C9⋊C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 1);