Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C31 · Schur multiplier (H2) = C2 |
| direct product | C31×#359 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C31 | D8 |
| commutator | C8 | C2×C4×C31 |
| Frattini, cosocle | C2×C8 | C22×C31 |
| socle | C2×C31 | #102 |
| prime radical | C31×#135 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C31 ◁ C2×C4×C31 ◁ C2×C8×C31 ◁ G | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 2 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)(32,33,36,41,38,42,37,52)(34,43,45,59,46,60,53,57)(35,47,49,58,51,62,50,40)(39,48,54,61,56,63,55,44);(32,34)(33,39)(35,48)(36,45)(37,53)(38,46)(40,57)(41,54)(42,56)(43,47)(44,50)(49,61)(51,63)(52,55)(58,59)(60,62)682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 40);