Finite Group DatabasebetaFinite Group Databasebeta| order | 4510 |
| automorphism | Aut(G) order 3608000 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2255 |
| unambiguous semidirect product | C5⋊D451 |
| unambiguous semidirect product | C11⋊D205 |
| unambiguous semidirect product | C41⋊D55 |
| Fitting, socle, derived, Hall | C5×C11×C41 ⋊ C2 |
| Hall | C11×C41 ⋊ D5 |
| Hall | C5×C41 ⋊ D11 |
| Hall | C5×C11 ⋊ D41 |
| Sylow | C41 ⋊ D55 |
| Sylow | C11 ⋊ D205 |
| Sylow | C5 ⋊ D451 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C11×C41 | C2 |
| LCS | G ▷ C5×C11×C41 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2255 |
Polycyclic presentation:
2,5,11,41|b^a=b^4,c^a=c^10,d^a=d^401129 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2255, D6765, D11275, … |
| maximal normal subgroup of | C3×D2255, C5⋊#17985247, C5⋊#17985250, … |
| maximal quotient of | C3×D2255, D6765, D11275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4510, 14);