Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C25 · Schur multiplier (H2) = C2 |
| direct product | C25×Dic3⋊C4 |
| unambiguous semidirect product | Dic3⋊(C4×C25) |
| Hall | C3×C25 ⋊ C4⋊C4 |
| Sylow | C3 ⋊ C4⋊C4×C25 |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 1200 |
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, 57);