Finite Group DatabasebetaFinite Group Databasebeta| order | 1500 |
| isoclinism | isoclinic class of D3×D125 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D125 |
| unambiguous semidirect product | (D3×C125)⋊C2 |
| unambiguous semidirect product | (C3×D125)⋊C2 |
| unambiguous semidirect product | D375⋊C2 |
| Fitting, derived, Hall | C3×C125 ⋊ C22 |
| Sylow | C125 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D125 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C125 | C22 |
| Frattini | C25 | D3×D5 |
| socle | C3×C5 | C2×D25 |
| LCS | G ▷ C3×C125 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 128 |
| transitive degree | μt(G) = 375 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1500, 7);