Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#16861480 |
| Fitting, Hall | C3×C25×C41 ⋊ C4 |
| derived, Hall | C25×C41 ⋊ C3×C4 |
| Hall | C3×C41 ⋊ #1035 |
| Hall | C3×C25 ⋊ #4223 |
| Sylow | C41 ⋊ C3×#1035 |
| Sylow | C25 ⋊ C3×#4223 |
36 conjugacy classes of subgroups.
780 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#16861480, C32×#16861480, C3×C3⋊#16861480 |
| maximal normal subgroup of | C9×#16861480, C32×#16861480 |
| maximal quotient of | C9×#16861480, C32×#16861480, C3×C3⋊#16861480 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 24);