Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C31 · Schur multiplier (H2) = C2 |
| direct product | C31×Q8⋊C8 |
| unambiguous semidirect product | Q8⋊(C8×C31) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C31 | D4 |
| commutator | C4 | C2×C8×C31 |
| Frattini, cosocle | C42 | C22×C31 |
| socle, prime radical | C22×C31 | C22⋊C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C31 ◁ C42×C31 ◁ G | |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1984 |
A minimal faithful permutation representation — 2 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)(33,36)(34,38)(37,39)(40,41,42,44,43,45,46,47);(32,33,35,37)(34,39,38,36)868 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 7);