Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C25×D36 |
| unambiguous semidirect product | C4⋊(D9×C25) |
| Fitting | C4×C9×C25 ⋊ C2 |
| Hall | C9×C25 ⋊ D4 |
| Sylow | C9 ⋊ D4×C25 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 900 |
A minimal faithful permutation representation — 2 generators on 38 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)(26,27,28,29)(30,31,32,33,34,35,36,37,38);(27,29)(31,38)(32,37)(33,36)(34,35)525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 22);