Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of #6308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C33 |
| direct product | C5×#6312 |
| Fitting | C22×C33×C5 ⋊ C2 |
| Hall | C33×C5 ⋊ D4 |
| Sylow | C33 ⋊ C5×D4 |
448 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 540 |
A minimal faithful permutation representation — 4 generators on 18 points:
(1,2,3,4,5)(7,9)(16,17,18);(6,7)(8,9)(11,12)(14,15)(17,18);(13,14,15);(10,11,12)285 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 478);