Finite Group DatabasebetaFinite Group Databasebeta| order | 4598 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊D209 |
| unambiguous semidirect product | C19⋊(C11⋊D11) |
| Fitting, socle, derived, Hall | C112×C19 ⋊ C2 |
| Sylow | C112 ⋊ D19 |
| Sylow | C19 ⋊ C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C19 | C2 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2299 |
Polycyclic presentation:
2,11^2,19|b^a=b^10,c^a=c^10,d^a=d^181151 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11⋊(C11⋊(D19⋊C3)), #28352261, #28352263, … |
| maximal normal subgroup of | C11⋊(C11⋊(D19⋊C3)), #28352261, #28352263, … |
| maximal quotient of | C3⋊(C11⋊D209), C3×C11⋊D209, C5×C11⋊D209, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4598, 10);