Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#131⋊C9 |
| unambiguous semidirect product | #131⋊(C5×C9) |
| unambiguous semidirect product | (C5×#131)⋊C9 |
| Hall | C5×#131 ⋊ C9 |
| Sylow | #131 ⋊ C5×C9 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
420 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 660);