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×#358 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C31 | D8 |
| commutator | C8 | C2×C4×C31 |
| Frattini, cosocle | C2×C8 | C22×C31 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C2×C4×C31 ◁ C2×C8×C31 ◁ G | |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1984 |
A minimal faithful permutation representation — 2 generators on 51 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)(37,41)(38,44)(39,46)(42,51)(43,50)(45,48)(47,49);(36,37,40,43)(38,45,47,51)(39,48,46,42)(41,49,50,44)682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 39);