Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | C3×#27134245 |
| Fitting, socle | C3×C52×C41 ⋊ Dic3 |
| derived | C41×C52⋊C3 ⋊ C3×C4 |
| Hall | C3×C41×C52⋊C3 ⋊ C4 |
| Hall | C52×C41 ⋊ C3×Dic3 |
| Hall | C3×C52⋊C3 ⋊ Dic41 |
| Sylow | C41 ⋊ C3×#64480 |
| Sylow | C52 ⋊ C3×Dic123 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1845 |
624 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 399);