Finite Group DatabasebetaFinite Group Databasebeta| order | 4470 |
| automorphism | Aut(G) order 2646240 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2235 |
| unambiguous semidirect product | C3⋊D745 |
| unambiguous semidirect product | C5⋊D447 |
| unambiguous semidirect product | C149⋊D15 |
| Fitting, socle, derived, Hall | C3×C5×C149 ⋊ C2 |
| Hall | C5×C149 ⋊ D3 |
| Hall | C3×C149 ⋊ D5 |
| Sylow | C149 ⋊ D15 |
| Hall | C3×C5 ⋊ D149 |
| Sylow | C5 ⋊ D447 |
| Sylow | C3 ⋊ D745 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C149 | C2 |
| LCS | G ▷ C3×C5×C149 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 157 |
| transitive degree | μt(G) = 2235 |
Polycyclic presentation:
2,3,5,149|b^a=b^2,c^a=c^4,d^a=d^1481119 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D6705, C3⋊D2235, C3×D2235, … |
| maximal normal subgroup of | C3×D2235, C5×D2235, C7×D2235 |
| maximal quotient of | D6705, C3⋊D2235, C3×D2235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4470, 8);