Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C5 |
| direct product | C22×C4×C52⋊C3 |
| Fitting, Hall | C22×C4×C52 ⋊ C3 |
| derived, Sylow | C52 ⋊ C22×C3×C4 |
162 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2)(9,10,12)(11,15,17)(13,18,21)(14,20,23)(16,19,22);(3,4)(9,11,16,21,23)(10,15,19,13,14)(12,18,17,20,22);(5,6,7,8)176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 875);