Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of C3⋊(#41⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C3⋊(#41⋊C3) |
| unambiguous semidirect product | C3⋊(C11×#41⋊C3) |
| unambiguous semidirect product | #239⋊(C3×C11) |
| unambiguous semidirect product | (C11×#239)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D3×A4 |
| commutator, cosocle, hypocenter | C3×Q8 | C2×C3×C11 |
| Frattini | C2 | D3×C11×A4 |
| Fitting | C3×Q8×C11 | C2×C3 |
| socle | C2×C3×C11 | C2×A4 |
| LCS | G ▷ C3×Q8 | |
| UCS | C1 ◁ C2×C11 | |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 528 |
A minimal faithful permutation representation — 2 generators on 30 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,19)(14,24,23,25,20,18,21,26,15,17,22,27)(29,30);(12,22,16,20)(13,26,19,24)(14,15,21,23)(17,18,25,27)(28,29,30)231 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 458);