Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Q8⋊C9 |
| unambiguous semidirect product | Q8⋊(C9×C11) |
| unambiguous semidirect product | (Q8×C11)⋊C9 |
| derived, Sylow | Q8 ⋊ C9×C11 |
| Hall | Q8×C11 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical, hypercenter | C2×C3×C11 | A4 |
| commutator, hypocenter | Q8 | C9×C11 |
| Frattini | C2×C3 | C11×A4 |
| Fitting | C3×Q8×C11 | C3 |
| cosocle | C3×Q8 | C3×C11 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C2×C3×C11 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 792 |
231 conjugacy classes — view the full character table.
| derived subgroup of | C11⋊#3688, C11⋊#3689 |
| maximal subgroup of | C11×#3688, C11×#3689, C11⋊#3688, … |
| maximal normal subgroup of | C11×#3688, C11×#3689, C11⋊#3688, … |
| maximal quotient of | C2×C11×Q8⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 12);