Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C25 |
| direct product | C22×SD16×C31 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | D4 |
| commutator, Frattini, cosocle | C4 | C24×C31 |
| prime radical | C22×D4×C31 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ C22×C4×C31 ◁ G | |
298 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(3,4);(5,6,7,8,9,10,11,12);(6,8)(7,11)(10,12)868 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 251);