Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | C3×#10597159 |
| Fitting | C22×C32×C52 ⋊ C2 |
| Hall | C32×C52 ⋊ D4 |
| Sylow | C52 ⋊ C3×#67 |
| Sylow | C32 ⋊ C22⋊(C5⋊D5) |
296 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 300 |
459 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#67×C5⋊D5, #72231387, #72231392, … |
| maximal normal subgroup of | C3×#67×C5⋊D5, #72231387, #72231392, … |
| maximal quotient of | C2×C3×#10597159 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 536);