Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C31 · Schur multiplier (H2) = C22 |
| direct product | C31×#341 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C31 | D4 |
| commutator | C4 | C42×C31 |
| Frattini, cosocle | C22×C4 | C22×C31 |
| socle | C22×C31 | C4⋊C4 |
| prime radical | C23×C31 | Q8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ G | |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 2 generators on 51 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)(36,37,39,44,41,45,40,43)(38,46,47,42,49,50,48,51);(33,35)(36,38,40,48,41,49,39,47)(37,42,44,50,45,51,43,46)868 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 22);