Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of Dic30 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#1220 |
| Fitting | C22×C32×C52 ⋊ C2 |
| Hall | C32×C52 ⋊ D4 |
| Sylow | C52 ⋊ C3×#67 |
| Sylow | C32 ⋊ C5×C22⋊D5 |
208 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
495 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#11925664, C5×#10624236, #72224617, … |
| maximal normal subgroup of | C3×#11925664, C5×#10624236, #72224617, … |
| maximal quotient of | C2×C3×C5×#1220, C5×#67099⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 531);