Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#627 |
| Hall | C32×C11 ⋊ Q8 |
| Sylow | C32 ⋊ Q8×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D32 |
| commutator, cosocle | C2×C32 | C22×C11 |
| Frattini | C2 | D32×C11 |
| Fitting, socle, prime radical | C2×C32×C11 | C22 |
| hypocenter | C32 | Q8×C11 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C11 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | C11×#3775, C11×#3776, #13097229, … |
| maximal normal subgroup of | C11×#3775, C11×#3776, #13097229, … |
| maximal quotient of | C11×Dic3⋊Dic3, C11×#3724, C2×C11×#627 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 66);