Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C31 · Schur multiplier (H2) = C22 |
| direct product | C31×#430 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C31 | C2×D4 |
| commutator | C4 | C22×C4×C31 |
| Frattini, cosocle | C2×C4 | C23×C31 |
| socle | C2×C31 | C2×C4⋊C4 |
| prime radical | C23×C31 | Q8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C31 ◁ C22×C4×C31 ◁ G | |
102 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)(32,33,36,39,37,40,35,45)(34,41,44,46,42,47,43,38);(32,34,35,43,37,42,36,44)(33,38,39,41,40,46,45,47);(34,42)(38,46)(41,47)(43,44)682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 111);