Finite Group DatabasebetaFinite Group Databasebeta| order | 1500 |
| isoclinism | isoclinic class of D125 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D125 |
| unambiguous semidirect product | C125⋊(C22×C3) |
| unambiguous semidirect product | (C2×C125)⋊(C2×C3) |
| Fitting | C2×C3×C125 ⋊ C2 |
| derived, Sylow | C125 ⋊ C22×C3 |
| Hall | C3×C125 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D125 |
| commutator, cosocle, hypocenter | C125 | C22×C3 |
| Frattini | C25 | C2×C3×D5 |
| Fitting | C2×C3×C125 | C2 |
| socle | C2×C3×C5 | D25 |
| LCS | G ▷ C125 | |
| UCS | C1 ◁ C2×C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 750 |
384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1500, 9);