Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D75 |
| unambiguous semidirect product | (C2×C3)⋊(C7×D25) |
| unambiguous semidirect product | (C2×C25)⋊(D3×C7) |
| Fitting | C2×C3×C7×C25 ⋊ C2 |
| derived, Hall | C3×C25 ⋊ C22×C7 |
| Hall | C3×C7×C25 ⋊ C22 |
| 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 | C2×C7 | D75 |
| commutator, cosocle, hypocenter | C3×C25 | C22×C7 |
| Frattini | C5 | C2×C7×D15 |
| Fitting | C2×C3×C7×C25 | C2 |
| socle | C2×C3×C5×C7 | D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C2×C7 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1050 |
546 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C49×D75, C7×D7×D75, C2×C72×D75, … |
| maximal normal subgroup of | C2×C49×D75, C2×C72×D75, C2×C7×C11×D75, … |
| maximal quotient of | C2×C49×D75, C7×D7×D75, C2×C72×D75, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 39);