Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2 |
| direct product | D3×C11×Dic3 |
| unambiguous semidirect product | (C3×D3)⋊(C4×C11) |
| derived, Sylow | C32 ⋊ C2×C4×C11 |
| Hall | C32×C11 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D32 |
| commutator, hypocenter | C32 | C2×C4×C11 |
| Frattini | C2 | D32×C11 |
| Fitting, socle | C2×C32×C11 | C22 |
| prime radical | C2×C3×D3×C11 | C2 |
| cosocle | C2×C32 | C22×C11 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C11 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | D3×Dic3×D11, D3×D33⋊C4, D3×#63141, … |
| maximal normal subgroup of | D3×Dic3×D11, D3×D33⋊C4, D3×#63141, … |
| maximal quotient of | D3×C11×C3⋊C8, C11×#3711, C11×Dic32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 62);