Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#6441 |
| Hall | C5×C7 ⋊ C22⋊Q8 |
| Sylow | C7 ⋊ C5×C22⋊Q8 |
148 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 560 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7,9,11,12,10,8)(14,16)(17,19,20,24)(18,21,22,23);(13,14)(15,16);(7,8)(9,10)(11,12)(17,18,20,22)(19,23,24,21)220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 642);