Finite Group DatabasebetaFinite Group Databasebeta| order | 4510 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊D41 |
| Fitting, socle, derived, Hall | C11×C41 ⋊ C2×C5 |
| Hall | C41×C11⋊C5 ⋊ C2 |
| Hall | D451 ⋊ C5 |
| Hall | C11⋊C5 ⋊ D41 |
| Sylow | C41 ⋊ AGL(1,𝔽11) |
| Sylow | C11 ⋊ C5×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C41 | C2×C5 |
| LCS | G ▷ C11×C41 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 52 |
| transitive degree | μt(G) = 451 |
Polycyclic presentation:
2,5,11,41|c^a=c^10,d^a=d^40,c^b=c^4151 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4510, 28);