Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C31 · Schur multiplier (H2) = C2×C42 |
| direct product | C31×#376 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C31 | C22 |
| commutator | C2 | C2×C42×C31 |
| Frattini, cosocle | C23 | C23×C31 |
| socle, prime radical | C23×C31 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C31 ◁ G | |
178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1984 |
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)(32,33,34,35)(40,41)(42,45)(43,44)(46,47);(36,37,38,39)(41,44)(45,47);(40,42,43,46)(41,45,44,47)1240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 57);