Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of C11⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C11⋊#622 |
| derived, Hall | C32×C11 ⋊ C8 |
| Sylow | C11 ⋊ #622 |
| Sylow | C32 ⋊ C11⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊#157 |
| commutator, hypocenter | C32×C11 | C8 |
| Fitting, socle, prime radical | C2×C32×C11 | C4 |
| cosocle | C11×C3⋊Dic3 | C2 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^3,3^2,11|a^2=b,b^2=c,d^a=e,e^a=d^2,f^a=f^10,d^b=d^2,e^b=e^272 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#622, #13097217, #13097218, … |
| maximal normal subgroup of | D11×#622, #13097217, #13097218, … |
| maximal quotient of | C11⋊#3708, C2×C11⋊#622 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 47);