Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of AΣL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C31 · Schur multiplier (H2) = C2 |
| direct product | C31×#352 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | #99 |
| commutator | C23 | C2×C4×C31 |
| Frattini, cosocle | C2×D4 | C22×C31 |
| prime radical | C2×D4×C31 | C22 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C22×C31 ◁ C2×D4×C31 ◁ G | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 496 |
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)(32,33)(34,40)(35,43,44,38)(36,39)(37,41,45,47)(42,46);(32,34,36,42)(33,37,39,45)(35,41,44,47)(38,40,43,46)403 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 33);