Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×C11×C3⋊C8 |
| unambiguous semidirect product | C3⋊(C3×C8×C11) |
| derived | C3 ⋊ C3×C8×C11 |
| Hall | C32×C11 ⋊ C8 |
| Sylow | C32 ⋊ C8×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4×C11 | D3 |
| commutator, hypocenter | C3 | C3×C8×C11 |
| Frattini | C4 | C3×D3×C11 |
| Fitting | C32×C4×C11 | C2 |
| socle, prime radical | C2×C32×C11 | C4 |
| cosocle | C3×C4 | C2×C3×C11 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C3×C4×C11 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
396 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D11×C3⋊C8, C3×D33⋊C8, C3×#10587138, … |
| maximal normal subgroup of | C3×D11×C3⋊C8, C3×D33⋊C8, C3×#10587138, … |
| maximal quotient of | C3×C11×C3⋊C16, C2×C3×C11×C3⋊C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 32);