Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of D9×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D99⋊C4 |
| derived, Hall | C9×C11 ⋊ C2×C4 |
| Sylow | C11 ⋊ C4×D9 |
| Sylow | C9 ⋊ C4×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×D11 |
| commutator, hypocenter | C9×C11 | C2×C4 |
| Frattini | C2×C3 | D3×D11 |
| Fitting, cosocle | C2×C9×C11 | C22 |
| socle | C2×C3×C11 | C2×D3 |
| prime radical | C2×D99 | C2 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 396 |
Polycyclic presentation:
2^3,3,11,3|a^2=c,b^2=c,d^3=f,e^a=e^10,d^b=d^2f^2,f^b=f^284 conjugacy classes — view the full character table.
| maximal subgroup of | #13096940, D99⋊Q8, #13096947, … |
| maximal normal subgroup of | #13096940, D99⋊Q8, #13096947, … |
| maximal quotient of | D99⋊C8, #13096844, Dic9×Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 7);