Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#611 |
| Fitting | C22×C9×C11 ⋊ C2 |
| Hall | C9×C11 ⋊ D4 |
| Sylow | C9 ⋊ D4×C11 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C11 | C2×D9 |
| commutator, cosocle | C2×C9 | C22×C11 |
| Frattini | C2×C3 | C2×D3×C11 |
| Fitting | C22×C9×C11 | C2 |
| socle | C2×C3×C11 | C2×D3 |
| hypercenter | C22×C11 | D9 |
| hypocenter | C9 | D4×C11 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C11 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 396 |
231 conjugacy classes — view the full character table.
| maximal subgroup of | #13096954, #13096959, D11×#611, … |
| maximal normal subgroup of | #13096954, #13096959, D11×#611, … |
| maximal quotient of | C11×Dic9⋊C4, C11×(C2×D9)⋊C4, C11×#3672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 22);