Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×Dic11 |
| unambiguous semidirect product | (C2×C11)⋊(C32×C4) |
| derived, Sylow | C11 ⋊ C2×C32×C4 |
| Hall | C32×C11 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | D11 |
| commutator, hypocenter | C11 | C2×C32×C4 |
| Frattini | C2 | C2×C32×D11 |
| Fitting, socle, prime radical | C22×C32×C11 | C2 |
| cosocle | C2×C11 | C22×C32 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C22×C32 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 792 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 83);