Finite Group DatabasebetaFinite Group Databasebeta| order | 4610 |
| automorphism | Aut(G) order 4241200 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2305 |
| unambiguous semidirect product | C5⋊D461 |
| unambiguous semidirect product | C461⋊D5 |
| Fitting, socle, derived, Hall | C5×C461 ⋊ C2 |
| Sylow | C461 ⋊ D5 |
| Sylow | C5 ⋊ D461 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C461 | C2 |
| LCS | G ▷ C5×C461 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 466 |
| transitive degree | μt(G) = 2305 |
Polycyclic presentation:
2,5,461|b^a=b^4,c^a=c^4601154 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2305, D6915, D11525, … |
| maximal normal subgroup of | C3×D2305, C5⋊(D461⋊C5), C5×D2305, … |
| maximal quotient of | C3×D2305, D6915, D11525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4610, 5);