Finite Group DatabasebetaFinite Group Databasebeta| order | 1980 |
| isoclinism | isoclinic class of #4380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×#4380 |
| Fitting, socle, Hall | C32×C5×C11 ⋊ C4 |
| derived, Hall | C32×C5 ⋊ C4×C11 |
| Hall | C32×C11 ⋊ AGL(1,𝔽5) |
| Hall | C5×C11 ⋊ #157 |
| Sylow | C32 ⋊ C11×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C11×#157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #4380 |
| commutator, hypocenter | C32×C5 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C11 | C4 |
| prime radical | C11×C3⋊D15 | C2 |
| cosocle | C3⋊D15 | C2×C11 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C11 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 330 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,16,17,15)(19,20,21,22);(12,14,17)(13,16,15)(18,19,20,22,21)165 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C11×#4380, C11×C7⋊#4380, C121×#4380, … |
| maximal normal subgroup of | C7×C11×#4380, C121×#4380, C112×#4380, … |
| maximal quotient of | C7×C11×#4380, C11×C7⋊#4380, C121×#4380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1980, 81);