Finite Group DatabasebetaFinite Group Databasebeta| order | 1980 |
| isoclinism | isoclinic class of C3⋊D165 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊Dic165 |
| unambiguous semidirect product | C11⋊(C3⋊Dic15) |
| derived, Hall | C32×C5×C11 ⋊ C4 |
| Hall | C32×C11 ⋊ Dic5 |
| Hall | C5×C11 ⋊ C3⋊Dic3 |
| Hall | C32×C5 ⋊ Dic11 |
| Sylow | C11 ⋊ C3⋊Dic15 |
| Sylow | C32 ⋊ Dic55 |
| Sylow | C5 ⋊ C3⋊Dic33 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D165 |
| commutator, hypocenter | C32×C5×C11 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C32×C5×C11 | C2 |
| LCS | G ▷ C32×C5×C11 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1980 |
Polycyclic presentation:
2^2,3^2,5,11|a^2=b,c^a=c^2,d^a=d^2,e^a=e^4,f^a=f^10498 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C3⋊Dic165, C3⋊Dic1155, C3⋊Dic1815, … |
| maximal normal subgroup of | C7×C3⋊Dic165, C11×C3⋊Dic165, C13×C3⋊Dic165, … |
| maximal quotient of | C7×C3⋊Dic165, C3⋊Dic1155, C3⋊Dic1815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1980, 55);