Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of #1132 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#6392 |
| Hall | C5×C7 ⋊ #107 |
| Sylow | C7 ⋊ C5×#107 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 1120 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5)(6,7,9,11,12,10,8)(17,18,22,24,20,23,19,21);(7,8)(9,10)(11,12)(13,14,15,16)(18,21)(19,22)(23,24)310 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 94);