Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C25 · Schur multiplier (H2) = C22 |
| direct product | C25×(C2×D3)⋊C4 |
| unambiguous semidirect product | (C2×D3)⋊(C4×C25) |
| Fitting | C2×C3×C4×C25 ⋊ C2 |
| Hall | C3×C25 ⋊ C22⋊C4 |
| Sylow | C3 ⋊ C22⋊C4×C25 |
102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 600 |
A minimal faithful permutation representation — 2 generators on 36 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)(34,36);(27,28)(33,34)(35,36)450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 59);