Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C52 · Schur multiplier (H2) = C22×C5 |
| direct product | C52×#235 |
| Fitting | C2×C3×C4×C52 ⋊ C2 |
| Hall | C3×C52 ⋊ #41 |
| Sylow | C3 ⋊ C52×#41 |
320 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 600 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3,4,5)(11,12,13)(15,19)(18,21);(6,7,8,9,10)(14,16,17,20)(15,18,19,21);(12,13)(14,15)(16,18)(17,19)(20,21)450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 908);