Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×#14559049 |
| derived | #10597245 ⋊ C3×C4×C5 |
| Hall | C3×C5×#10597245 ⋊ C4 |
| Hall | C5×#10597245 ⋊ C3×C4 |
| Hall | C3×C112 ⋊ C5×Dic5 |
| Sylow | C112 ⋊ C3×C5×Dic5 |
120 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 660 |
930 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 371);