Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #87831 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#87831 |
| Hall | C3×C52 ⋊ C22⋊C4 |
| Sylow | C52 ⋊ C3×C22⋊C4 |
168 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 60 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,3)(5,7)(8,9)(11,12)(13,14,17,15,16);(4,5)(6,7)(9,10,11,12)(14,15,16,17)66 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11717375, D3×#87831, #72224584, … |
| maximal normal subgroup of | C3×#11717375, D3×#87831, #72224584, … |
| maximal quotient of | C3×#11925355, C32×#87831, C2×C3×#87831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 527);