Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D5×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#10597120 |
| derived | C3×C52 ⋊ C2×C3×C4 |
| Hall | C32×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ C3×C4×D3 |
| Sylow | C32 ⋊ #6036 |
184 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#6036, C3×#11925646, C3×#11925428, … |
| maximal normal subgroup of | C3×D3×#6036, C3×#11925646, C3×#11925428 |
| maximal quotient of | #72254576 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 430);