Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C11 |
| direct product | C5×(C11⋊Dic55)⋊C3 |
| unambiguous semidirect product | (C5×C11⋊Dic55)⋊C3 |
| derived | C5×C112 ⋊ C3×C4×C5 |
| Hall | C5×C11⋊Dic55 ⋊ C3 |
| Hall | C52×C112⋊C3 ⋊ C4 |
| Hall | C52×C112 ⋊ C3×C4 |
| Hall | C112⋊C3 ⋊ C5×Dic5 |
| Sylow | C112 ⋊ C3×C5×Dic5 |
| Sylow | C52 ⋊ (C11⋊Dic11)⋊C3 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 660 |
1120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 420);