Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#6769 |
| Hall | C3×C52 ⋊ #41 |
| Sylow | C52 ⋊ #239 |
| Sylow | C3 ⋊ C5×#709 |
192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
195 conjugacy classes — view the full character table.
| maximal subgroup of | #72230574, C5×D3×#709, #72230622, … |
| maximal normal subgroup of | #72230574, C5×D3×#709, #72230622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 781);