Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C5×#63780 |
| Hall | C32×C5 ⋊ #101 |
| Sylow | C32 ⋊ C5×#101 |
152 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)(6,8,11)(7,10,9)(12,14,16,22)(13,17,19,20)(15,23,24,21)(18,26,27,25);(6,7)(8,10,11,9)(12,13,15,18,16,19,24,27)(14,20,21,26,22,17,23,25)135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2649);