Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5×C11 |
| direct product | C3×C5×#14559052 |
| derived, Sylow | C112 ⋊ C3×C4×C52 |
| Hall | C3×C5×#10597245 ⋊ C4 |
| Hall | C5×#10597245 ⋊ C3×C4 |
| Hall | C3×C11⋊Dic11 ⋊ C52 |
| Hall | C11⋊Dic11 ⋊ C3×C52 |
| Hall | C3×C112 ⋊ C4×C52 |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3300 |
660 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 363);