Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C2 |
| direct product | C27×D20 |
| unambiguous semidirect product | C4⋊(D5×C27) |
| Fitting | C4×C5×C27 ⋊ C2 |
| Hall | C5×C27 ⋊ D4 |
| Sylow | C5 ⋊ D4×C27 |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 540 |
351 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 17);