Finite Group DatabasebetaFinite Group Databasebeta| order | 4609 |
| automorphism | ? |
| homology | Abelianization (H1) = C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C419⋊C11 |
| Fitting, socle, derived, Sylow | C419 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C419 | C11 |
| LCS | G ▷ C419 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 419 |
| transitive degree | μt(G) = 419 |
Polycyclic presentation:
11,419|b^a=b^33449 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C419⋊C11, C5×C419⋊C11, C7×C419⋊C11 |
| maximal normal subgroup of | C3×C419⋊C11, C5×C419⋊C11, C7×C419⋊C11 |
| maximal quotient of | C3×C419⋊C11, C5×C419⋊C11, C7×C419⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4609, 1);