Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #3774 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#63733 |
| Hall | C32×C5 ⋊ #108 |
| Sylow | C32 ⋊ C5×#108 |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3,4,5)(6,8)(7,10,11)(12,14,16,22,17,23,15,25)(13,18,19,26,20,27,24,21);(6,7)(8,11)(9,10)(12,13,16,19,17,20,15,24)(14,21,22,18,23,26,25,27)150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1878);