Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #3993 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×#3995 |
| Hall | C32×C5 ⋊ #108 |
| Sylow | C5 ⋊ C32×#108 |
180 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 720 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3)(7,8,9,11,10)(12,14,16,23,17,24,15,22)(13,18,19,21,20,26,25,27);(4,5,6)(8,9,10,11)(12,13,15,19,17,20,16,25)(14,21,22,26,24,27,23,18)198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2564);