Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | D3×C25×D17 |
| unambiguous semidirect product | (D3×C17)⋊(C2×C25) |
| unambiguous semidirect product | (C3×D17)⋊(C2×C25) |
| unambiguous semidirect product | D51⋊(C2×C25) |
| Fitting, Hall | C3×C17×C25 ⋊ C22 |
| derived, Hall | C3×C17 ⋊ C22×C25 |
| Hall | C17×C25 ⋊ C2×D3 |
| Hall | C3×C25 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D3×C25 |
| Sylow | C3 ⋊ C2×C25×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D3×D17 |
| commutator, hypocenter | C3×C17 | C22×C25 |
| Frattini | C5 | C5×D3×D17 |
| Fitting | C3×C17×C25 | C22 |
| socle | C3×C5×C17 | C22×C5 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C25 | |
60 conjugacy classes of subgroups.
750 conjugacy classes — view the full character table.
| maximal subgroup of | D9×C25×D17, C3×D3×C25×D17, C3⋊D3×C25×D17, … |
| maximal normal subgroup of | C3×D3×C25×D17, D3×C7×C25×D17 |
| maximal quotient of | D9×C25×D17, C3×D3×C25×D17, C3⋊D3×C25×D17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 23);