Finite Group DatabasebetaFinite Group Databasebeta| order | 5900 |
| automorphism | Aut(G) order 3422000 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2950 |
| direct product | C2×D1475 |
| unambiguous semidirect product | (C2×C25)⋊D59 |
| unambiguous semidirect product | (C2×C59)⋊D25 |
| Fitting | C2×C25×C59 ⋊ C2 |
| derived, Hall | C25×C59 ⋊ C22 |
| Sylow | C59 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×D59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1475 |
| commutator, hypocenter | C25×C59 | C22 |
| Frattini | C5 | C2×D295 |
| Fitting | C2×C25×C59 | C2 |
| socle | C2×C5×C59 | D5 |
| LCS | G ▷ C25×C59 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
1478 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1475, C2×D4425, C2×C3×D1475, … |
| maximal normal subgroup of | C2×C3×D1475, D5900 |
| maximal quotient of | D3×D1475, C2×D4425, C2×C3×D1475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5900, 11);