Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #63768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×#63770 |
| Hall | C32×C5 ⋊ #108 |
| Sylow | C32 ⋊ C5×#108 |
104 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)(12,14,16,23,17,24,15,22)(13,18,19,21,20,26,25,27);(6,7)(8,10,11,9)(12,13,15,19,17,20,16,25)(14,21,22,26,24,27,23,18)150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2639);