Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C23 |
| direct product | C31×#458 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | #120 |
| commutator, Frattini, cosocle | C23 | C23×C31 |
| prime radical | C31×H(5,𝔽2) | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C23×C31 ◁ G | |
160 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 496 |
A minimal faithful permutation representation — 3 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)(32,33,36,39)(34,37,41,44)(35,38,42,45)(40,46,47,43);(32,34)(33,37)(35,40)(36,41)(38,43)(39,44)(42,47)(45,46);(32,35)(33,38)(34,40)(36,42)(37,43)(39,45)(41,47)(44,46)496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 139);