Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C2 |
| direct product | C31×#499 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C31 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C31 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C42×C31 ◁ G | |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1984 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)(32,33,35,37)(34,38,39,36)(40,41,43,45)(42,48,49,55)(44,52,51,47)(46,54,53,50);(32,34,35,39)(33,36,37,38)(41,45)(46,53)(47,52)(48,55);(40,42,44,50,43,49,51,54)(41,46,47,48,45,53,52,55)682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 180);