Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of D3×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | D3×C7×D25 |
| unambiguous semidirect product | (D3×C25)⋊(C2×C7) |
| unambiguous semidirect product | (C3×D25)⋊(C2×C7) |
| unambiguous semidirect product | D75⋊(C2×C7) |
| Fitting, Hall | C3×C7×C25 ⋊ C22 |
| derived, Hall | C3×C25 ⋊ C22×C7 |
| Hall | C7×C25 ⋊ C2×D3 |
| Sylow | C25 ⋊ C2×D3×C7 |
| Hall | C3×C7 ⋊ C2×D25 |
| Sylow | C3 ⋊ C2×C7×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D3×D25 |
| commutator, cosocle, hypocenter | C3×C25 | C22×C7 |
| Frattini | C5 | D3×C7×D5 |
| Fitting | C3×C7×C25 | C22 |
| socle | C3×C5×C7 | C2×D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C7 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 525 |
294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C49×D25, D3×C72×D25, C7×D21×D25, … |
| maximal normal subgroup of | D3×C49×D25, D3×C72×D25, D3×C7×C11×D25, … |
| maximal quotient of | D3×C49×D25, D3×C72×D25, C7×D21×D25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 27);