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×#576 |
| 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 | |
268 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 496 |
A minimal faithful permutation representation — 4 generators on 47 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)(34,38)(35,37)(36,40)(39,43)(41,45)(42,44)(46,47);(33,37)(35,43)(38,44)(39,40)(42,47)(45,46);(32,34)(33,38)(35,42)(36,41)(37,44)(39,46)(40,45)(43,47);(34,41)(38,45)(42,47)(44,46)682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 257);