Finite Group DatabasebetaFinite Group Databasebeta| order | 1980 |
| isoclinism | isoclinic class of A4×C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C2 |
| derived, Hall | C22×C11 ⋊ C5×C9 |
| Hall | C11×C22⋊C9 ⋊ C5 |
| Hall | C22×C11⋊C5 ⋊ C9 |
| Sylow | C11 ⋊ C5×C22⋊C9 |
| Sylow | C22 ⋊ C9×C11⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | A4×C11⋊C5 |
| commutator, hypocenter | C22×C11 | C5×C9 |
| Fitting, socle, cosocle | C22×C3×C11 | C3×C5 |
| prime radical | C22×C3×C11⋊C5 | C3 |
| LCS | G ▷ C22×C11 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 198 |
A minimal faithful permutation representation — 2 generators on 24 points:
(2,3,4)(5,6,8,7,9,11,10,12,13)(15,16,18,21,20)(17,19,23,24,22);(1,4)(2,3)(14,15,17,20,16,18,22,24,19,21,23)84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1980, 14);