Finite Group DatabasebetaFinite Group Databasebeta| order | 4598 |
| automorphism | Aut(G) order 4552020 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2299 |
| unambiguous semidirect product | C19⋊D121 |
| unambiguous semidirect product | C121⋊D19 |
| Fitting, derived, Hall | C19×C121 ⋊ C2 |
| Sylow | C121 ⋊ D19 |
| Sylow | C19 ⋊ D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C19×C121 | C2 |
| Frattini | C11 | D209 |
| socle | C11×C19 | D11 |
| LCS | G ▷ C19×C121 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 140 |
| transitive degree | μt(G) = 2299 |
Polycyclic presentation:
2,11,19,11|b^11=d^10,b^a=b^10d,c^a=c^18,d^a=d^101151 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C19⋊C3)⋊D121, C3×D2299, D6897, … |
| maximal normal subgroup of | (C19⋊C3)⋊D121, C3×D2299, C5×D2299, … |
| maximal quotient of | C3×D2299, D6897, C5×D2299, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4598, 4);