Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C22 |
| direct product | C31×#400 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C31 | C23 |
| commutator, Frattini, cosocle | C23 | C23×C31 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1984 |
A minimal faithful permutation representation — 3 generators on 51 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)(38,42)(40,43)(44,45,47,49)(46,50,51,48);(33,35)(36,37,39,41)(38,43,42,40)(44,45)(46,50)(47,49)(48,51);(32,33)(34,35)(36,38)(37,40)(39,42)(41,43)(44,46,47,51)(45,48,49,50)682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 81);