Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×C4×D11 |
| Fitting | C32×C4×C11 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C32×C4 |
| Hall | C32×C11 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C4 | D11 |
| commutator, hypocenter | C11 | C2×C32×C4 |
| Frattini | C2 | C2×C32×D11 |
| Fitting | C32×C4×C11 | C2 |
| socle | C2×C32×C11 | C22 |
| prime radical | C2×C32×D11 | C2 |
| cosocle | C2×C11 | C22×C32 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C32×C4 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 396 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D11×C3⋊C8, C3×#10587138, D11×C3⋊(C3⋊C8), … |
| maximal normal subgroup of | C3×D11×C3⋊C8, C3×#10587138, D11×C3⋊(C3⋊C8), … |
| maximal quotient of | C32×C8×D11, C32×#4313, C32×C4×Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 81);