Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C5 |
| direct product | C2×Q8×C52⋊C3 |
| Fitting, Hall | C2×C52×Q8 ⋊ C3 |
| Sylow | C52 ⋊ C2×C3×Q8 |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2)(11,12,14)(13,17,19)(15,20,23)(16,22,25)(18,21,24);(3,4,5,6)(7,10,9,8)(11,13,18,23,25)(12,17,21,15,16)(14,20,19,22,24);(3,7,5,9)(4,8,6,10)110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 877);