Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×C25×D21 |
| unambiguous semidirect product | (C2×C3)⋊(D7×C25) |
| unambiguous semidirect product | (C2×C7)⋊(D3×C25) |
| Fitting | C2×C3×C7×C25 ⋊ C2 |
| derived, Hall | C3×C7 ⋊ C22×C25 |
| Hall | C3×C7×C25 ⋊ C22 |
| Hall | C7×C25 ⋊ C2×D3 |
| Hall | C3×C25 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D3×C25 |
| Sylow | C3 ⋊ C2×D7×C25 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1050 |
600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C25×D147, D7×C25×D21, C2×C7×C25×D21, … |
| maximal normal subgroup of | C2×C7×C25×D21, C2×C11×C25×D21, C2×C13×C25×D21, … |
| maximal quotient of | C2×C25×D147, D7×C25×D21, C2×C7×C25×D21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 38);