Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of D99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic99 |
| unambiguous semidirect product | (C2×C9)⋊Dic11 |
| unambiguous semidirect product | (C2×C11)⋊Dic9 |
| derived, Hall | C9×C11 ⋊ C2×C4 |
| Sylow | C11 ⋊ C2×Dic9 |
| Sylow | C9 ⋊ C2×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D99 |
| commutator, hypocenter | C9×C11 | C2×C4 |
| Frattini | C2×C3 | C2×D33 |
| Fitting | C22×C9×C11 | C2 |
| socle, prime radical | C22×C3×C11 | D3 |
| cosocle | C2×C9×C11 | C22 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C22 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 792 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | Dic9×Dic11, #13096860, Dic9⋊Dic11, … |
| maximal normal subgroup of | Dic9×Dic11, #13096860, Dic9⋊Dic11, … |
| maximal quotient of | C2×C9⋊(C11⋊C8), #13096905, C4×Dic99, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 26);