Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C41 · Schur multiplier (H2) = C1 |
| direct product | C3×C41×#1035 |
| Fitting, Hall | C3×C25×C41 ⋊ C4 |
| derived, Sylow | C25 ⋊ C3×C4×C41 |
| Hall | C25×C41 ⋊ C3×C4 |
| Hall | C3×C25 ⋊ C4×C41 |
36 conjugacy classes of subgroups.
1230 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C41×#1035, C32×C41×#1035, C3×C41×C3⋊#1035 |
| maximal normal subgroup of | C9×C41×#1035, C32×C41×#1035 |
| maximal quotient of | C9×C41×#1035, C32×C41×#1035, C3×C41×C3⋊#1035 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 23);