Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×Dic3⋊Dic3 |
| unambiguous semidirect product | Dic3⋊(C11×Dic3) |
| Hall | C32×C11 ⋊ C4⋊C4 |
| Sylow | C32 ⋊ C11×C4⋊C4 |
120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 528 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(17,19)(21,22)(23,24,25);(16,17,18,19)(20,21,22)(24,25)330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 232);