Finite Group DatabasebetaFinite Group Databasebeta| order | 1980 |
| isoclinism | isoclinic class of D99 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic99 |
| unambiguous semidirect product | C9⋊(C5×Dic11) |
| derived, Hall | C9×C11 ⋊ C4×C5 |
| Hall | C5×C9×C11 ⋊ C4 |
| Hall | C5×C11 ⋊ Dic9 |
| Hall | C5×C9 ⋊ Dic11 |
| Sylow | C11 ⋊ C5×Dic9 |
| Sylow | C9 ⋊ C5×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D99 |
| commutator, hypocenter | C9×C11 | C4×C5 |
| Frattini | C2×C3 | C5×D33 |
| Fitting | C2×C5×C9×C11 | C2 |
| socle, prime radical | C2×C3×C5×C11 | D3 |
| cosocle | C2×C9×C11 | C2×C5 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C2×C5 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1980 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3,4,5)(6,7)(8,9)(10,11,12,13,14,15,16,17,18)(19,20,21,22,23,24,25,26,27,28,29);(6,8,7,9)(11,18)(12,17)(13,16)(14,15)(20,29)(21,28)(22,27)(23,26)(24,25)510 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×Dic99, C5×Dic693, C5×Dic1089, … |
| maximal normal subgroup of | C5×C7×Dic99, C5×C11×Dic99, C5×C13×Dic99, … |
| maximal quotient of | C5×C7×Dic99, C5×Dic693, C5×Dic1089, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1980, 9);