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×#401 |
| 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 | |
118 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)(34,38)(36,39)(41,44)(45,46)(48,49,51,53)(50,54,55,52);(32,33,35,37)(34,39,38,36)(40,41,43,44)(42,46,47,45)(48,49)(50,54)(51,53)(52,55);(32,34)(33,36)(35,38)(37,39)(40,42,43,47)(41,45,44,46)(48,50,51,55)(49,52,53,54)682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 82);