Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C25 |
| direct product | C31×#578 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | C22×D4 |
| commutator, Frattini, cosocle | C4 | C24×C31 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ #41×C31 ◁ G | |
248 conjugacy classes of subgroups.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 4 generators on 63 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)(32,33,37,41)(34,42,45,55)(35,39,46,53)(36,48,50,40)(38,49,52,44)(43,56,57,63)(47,60,59,54)(51,61,62,58);(32,34,37,45)(33,38,41,52)(35,43,46,57)(36,49,50,44)(39,51,53,62)(40,55,48,42)(47,61,59,58)(54,63,60,56);(32,35)(33,39)(34,43)(36,47)(37,46)(38,51)(40,54)(41,53)(42,56)(44,58)(45,57)(48,60)(49,61)(50,59)(52,62)(55,63);(35,46)(39,53)(43,57)(47,59)(51,62)(54,60)(56,63)(58,61)682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 259);