Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D15⋊D17 |
| unambiguous semidirect product | D15⋊(C5×D17) |
| unambiguous semidirect product | D51⋊(C5×D5) |
| unambiguous semidirect product | D85⋊(C5×D3) |
| Fitting, socle, Hall | C3×C52×C17 ⋊ C22 |
| derived | C3×C5×C17 ⋊ C22×C5 |
| Hall | C52×C17 ⋊ C2×D3 |
| Hall | C3×C52 ⋊ C2×D17 |
| Hall | C3×C17 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ D3×D17 |
| Sylow | C17 ⋊ C5×D3×D5 |
| Sylow | C3 ⋊ C5×D5×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D15⋊D17 |
| commutator, hypocenter | C3×C5×C17 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C17 | C22 |
| LCS | G ▷ C3×C5×C17 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
420 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D45⋊D17, D51⋊#3874, C3×C5×D15⋊D17, … |
| maximal normal subgroup of | C3×C5×D15⋊D17, C5×C7×D15⋊D17 |
| maximal quotient of | C5×D45⋊D17, C3×C5×D15⋊D17, C5×D85⋊(C3⋊D3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 110);