Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of C3⋊D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊(C11⋊C8)) |
| unambiguous semidirect product | C11⋊(C3⋊(C3⋊C8)) |
| derived, Hall | C32×C11 ⋊ C8 |
| Sylow | C11 ⋊ C3⋊(C3⋊C8) |
| Sylow | C32 ⋊ C11⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | C3⋊D33 |
| commutator, hypocenter | C32×C11 | C8 |
| Fitting, cosocle | C32×C4×C11 | C2 |
| socle, prime radical | C2×C32×C11 | C4 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C4 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 792 |
Polycyclic presentation:
2^3,3^2,11|a^2=b,b^2=c,d^a=d^2,e^a=e^2,f^a=f^10204 conjugacy classes — view the full character table.
| maximal subgroup of | D11×C3⋊(C3⋊C8), C3⋊D3×C11⋊C8, #13097032, … |
| maximal normal subgroup of | D11×C3⋊(C3⋊C8), C3⋊D3×C11⋊C8, #13097032, … |
| maximal quotient of | C3⋊(C3⋊(C11⋊C16)), C2×C3⋊(C3⋊(C11⋊C8)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 35);