Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22×C5 |
| direct product | C22⋊C4×C52⋊C3 |
| unambiguous semidirect product | (C52×C22⋊C4)⋊C3 |
| Fitting, Hall | C52×C22⋊C4 ⋊ C3 |
| Sylow | C52 ⋊ C3×C22⋊C4 |
102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6)(3,5,7,8)(9,10,12)(11,15,17)(13,18,21)(14,20,23)(16,19,22);(2,5)(6,8)(9,11,16,21,23)(10,15,19,13,14)(12,18,17,20,22)110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 376);