Finite Group DatabasebetaFinite Group Databasebeta| order | 4700 |
| automorphism | Aut(G) order 2162000 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2350 |
| direct product | C2×D1175 |
| unambiguous semidirect product | (C2×C25)⋊D47 |
| unambiguous semidirect product | (C2×C47)⋊D25 |
| Fitting | C2×C25×C47 ⋊ C2 |
| derived, Hall | C25×C47 ⋊ C22 |
| Sylow | C47 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1175 |
| commutator, cosocle, hypocenter | C25×C47 | C22 |
| Frattini | C5 | C2×D235 |
| Fitting | C2×C25×C47 | C2 |
| socle | C2×C5×C47 | D5 |
| LCS | G ▷ C25×C47 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2350 |
1178 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1175, C2×D3525, C2×C3×D1175, … |
| maximal normal subgroup of | C2×C3×D1175, C2×C7×D1175, D4700 |
| maximal quotient of | D3×D1175, C2×D3525, C2×C3×D1175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4700, 11);