Finite Group DatabasebetaFinite Group Databasebeta| order | 1476 |
| isoclinism | isoclinic class of C9⋊#4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#4223 |
| Fitting, derived, Hall | C9×C41 ⋊ C4 |
| Sylow | C41 ⋊ Dic9 |
| Sylow | C9 ⋊ #4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C41 | C4 |
| Frattini | C3 | C3⋊#4223 |
| socle | C3×C41 | Dic3 |
| prime radical | C3×D41 | D3 |
| cosocle | C9×D41 | C2 |
| LCS | G ▷ C9×C41 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 369 |
Polycyclic presentation:
2^2,3,41,3|a^2=b,c^3=e^2,c^a=c^2e,d^a=d^32,e^a=e^2,d^b=d^40102 conjugacy classes — view the full character table.
| maximal subgroup of | C11×C9⋊#4223, C9⋊(C11⋊#4223), C13×C9⋊#4223, … |
| maximal normal subgroup of | C11×C9⋊#4223, C13×C9⋊#4223, C17×C9⋊#4223, … |
| maximal quotient of | C11×C9⋊#4223, C9⋊(C11⋊#4223), C13×C9⋊#4223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1476, 6);