Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#3811 |
| Fitting | C22×C32×C11 ⋊ C22 |
| Hall | C32×C11 ⋊ C2×D4 |
| Sylow | C32 ⋊ C2×D4×C11 |
248 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 132 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,18)(19,20,21);(13,15)(17,18);(13,15)(20,21)264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×#3811, C11⋊C5×#3811 |
| maximal normal subgroup of | D11×#3811, C11⋊C5×#3811 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 549);