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) = C23 |
| direct product | C2×C31×#97 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C31 | C22 |
| commutator | C2 | C2×C42×C31 |
| Frattini, cosocle | C2×C4 | C23×C31 |
| socle, prime radical | C23×C31 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C31 ◁ G | |
146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1984 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(7,8,9,12,10,11,13,14);(3,4,5,6)(8,11)(12,14)1240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 84);