Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×#1094 |
| Hall | C23×C5 ⋊ 3−1+2 |
| Sylow | C23 ⋊ C5×3−1+2 |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C5×#1094, C2×D5×#1094, C2×C5×((C22⋊C9)⋊C2)⋊C3, … |
| maximal normal subgroup of | C22×C5×#1094, C2×D5×#1094, C2×C5×((C22⋊C9)⋊C2)⋊C3, … |
| maximal quotient of | C22×C5×#1094 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 343);