Finite Group DatabasebetaFinite Group Databasebeta| order | 1980 |
| isoclinism | isoclinic class of C11⋊#4380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C11⋊#4380 |
| Fitting, socle, derived, Hall | C32×C5×C11 ⋊ C4 |
| Hall | C32×C11 ⋊ AGL(1,𝔽5) |
| Hall | C5×C11 ⋊ #157 |
| Hall | C32×C5 ⋊ Dic11 |
| Sylow | C11 ⋊ #4380 |
| Sylow | C32 ⋊ C11⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C11⋊#157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C11 | C4 |
| prime radical, cosocle | C11×C3⋊D15 | C2 |
| LCS | G ▷ C32×C5×C11 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
Polycyclic presentation:
2^2,3^2,5,11|a^2=b,c^a=cd^2,d^a=c^2d^2,e^a=e^2,f^a=f^10,c^b=c^2,d^b=d^2,e^b=e^4135 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C11⋊#4380, C7⋊(C11⋊#4380), C121⋊#4380, … |
| maximal normal subgroup of | C7×C11⋊#4380, C11×C11⋊#4380, C13×C11⋊#4380, … |
| maximal quotient of | C7×C11⋊#4380, C7⋊(C11⋊#4380), C121⋊#4380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1980, 82);