Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of #3688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#3688 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | (C22⋊C9)⋊C2 |
| commutator, cosocle, hypocenter | Q8⋊C9 | C2×C11 |
| Frattini | C2×C3 | C11×S4 |
| Fitting | C3×Q8×C11 | D3 |
| socle, prime radical | C2×C3×C11 | S4 |
| LCS | G ▷ Q8⋊C9 | |
| UCS | C1 ◁ C2×C11 | |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 1584 |
A minimal faithful permutation representation — 2 generators on 36 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,17,21,24,16,26,23,18)(13,22,25,15,19,14,27,20)(29,31)(30,34)(32,33)(35,36);(14,20,23)(15,21,22)(17,24,27)(18,25,26)(28,36,31,34,33,32,30,29,35)165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 93);