Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | Aut(G) order 1632000 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2550 |
| direct product | C2×D1275 |
| unambiguous semidirect product | (C2×C3)⋊D425 |
| unambiguous semidirect product | (C2×C17)⋊D75 |
| unambiguous semidirect product | (C2×C25)⋊D51 |
| Fitting | C2×C3×C17×C25 ⋊ C2 |
| derived, Hall | C3×C17×C25 ⋊ C22 |
| Hall | C17×C25 ⋊ C2×D3 |
| Hall | C3×C25 ⋊ C2×D17 |
| Hall | C3×C17 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×D51 |
| Sylow | C17 ⋊ C2×D75 |
| Sylow | C3 ⋊ C2×D425 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1275 |
| commutator, hypocenter | C3×C17×C25 | C22 |
| Frattini | C5 | C2×D255 |
| Fitting | C2×C3×C17×C25 | C2 |
| socle | C2×C3×C5×C17 | D5 |
| LCS | G ▷ C3×C17×C25 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
1278 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3825, D3×D1275, C2×C3⋊D1275, … |
| maximal normal subgroup of | C2×C3×D1275, C2×C7×D1275, D5100 |
| maximal quotient of | C2×D3825, D3×D1275, C2×C3⋊D1275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 36);