Finite Group DatabasebetaFinite Group Databasebeta| order | 1500 |
| isoclinism | isoclinic class of C3⋊(D25⋊C5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊(D25⋊C5) |
| unambiguous semidirect product | (C2×C3)⋊(D25⋊C5) |
| unambiguous semidirect product | (C2×5−1+2)⋊D3 |
| unambiguous semidirect product | (C2×D75)⋊C5 |
| Fitting | C2×C3×5−1+2 ⋊ C2 |
| derived | C3×C25 ⋊ C22×C5 |
| Hall | C3×5−1+2 ⋊ C22 |
| Sylow | 5−1+2 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D25⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(D25⋊C5) |
| commutator, cosocle, hypocenter | C3×C25 | C22×C5 |
| Frattini | C5 | C2×C5×D15 |
| Fitting | C2×C3×5−1+2 | C2 |
| socle | C2×C3×C5 | C5×D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C2 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 150 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×D25⋊C5, D3×C3⋊(D25⋊C5) |
| maximal normal subgroup of | C2×D3×D25⋊C5 |
| maximal quotient of | D3×C3⋊(D25⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1500, 92);