Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of #63140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#63142 |
| Hall | C32×C11 ⋊ D4 |
| Sylow | C11 ⋊ C3×D12 |
| Sylow | C32 ⋊ C22⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D3×D11 |
| commutator, cosocle | C2×C3×C11 | C22×C3 |
| Frattini | C2 | C3×D3×D11 |
| Fitting, socle | C2×C32×C11 | C22 |
| hypocenter | C3×C11 | C3×D4 |
| LCS | G ▷ C2×C3×C11 ▷ C3×C11 | |
| UCS | C1 ◁ C2×C3 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63142, #13097255, #13097256, … |
| maximal normal subgroup of | D3×#63142, #13097255, #13097256, … |
| maximal quotient of | C3×#10587143, C3×#10587148, C3×#10587149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 53);