Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C3 |
| direct product | C32×C11⋊C8 |
| unambiguous semidirect product | C11⋊(C32×C8) |
| derived, Sylow | C11 ⋊ C32×C8 |
| Hall | C32×C11 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C4 | D11 |
| commutator, hypocenter | C11 | C32×C8 |
| Frattini | C4 | C32×D11 |
| Fitting | C32×C4×C11 | C2 |
| socle, prime radical | C2×C32×C11 | C4 |
| cosocle | C4×C11 | C2×C32 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C32×C4 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 792 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×C11⋊C8, C3×D33⋊C8, C3×#10587139, … |
| maximal normal subgroup of | C3×D3×C11⋊C8, C3×D33⋊C8, C3×#10587139, … |
| maximal quotient of | C32×C11⋊C16, C2×C32×C11⋊C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 31);