Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×Q64 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C2×C31 | D16 |
| commutator, Frattini, cosocle | C16 | C22×C31 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C4×C31 ◁ C8×C31 ◁ C16×C31 ◁ G | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 1984 |
A minimal faithful permutation representation — 2 generators on 95 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)(32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63)(64,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65);(32,64,48,80)(33,65,49,81)(34,66,50,82)(35,67,51,83)(36,68,52,84)(37,69,53,85)(38,70,54,86)(39,71,55,87)(40,72,56,88)(41,73,57,89)(42,74,58,90)(43,75,59,91)(44,76,60,92)(45,77,61,93)(46,78,62,94)(47,79,63,95)589 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 54);