Finite Group DatabasebetaFinite Group Databasebeta| order | 4598 |
| isoclinism | isoclinic class of D209 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D209 |
| unambiguous semidirect product | C11⋊(C11×D19) |
| unambiguous semidirect product | C19⋊(C11×D11) |
| Fitting, socle, Hall | C112×C19 ⋊ C2 |
| derived | C11×C19 ⋊ C2×C11 |
| Sylow | C112 ⋊ D19 |
| Sylow | C19 ⋊ C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D209 |
| commutator, cosocle, hypocenter | C11×C19 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C112×C19 | C2 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C11 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 418 |
1166 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×C11⋊(D19⋊C3), C19⋊#10624391, C11×D627, … |
| maximal normal subgroup of | C11×C11⋊(D19⋊C3), C3×C11×D209, C11×C19⋊AGL(1,𝔽11), … |
| maximal quotient of | C11×D627, C3×C11×D209, C5×C11×D209, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4598, 8);