Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C2×C4 |
| direct product | C31×#494 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C31 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C31 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C42×C31 ◁ G | |
122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1984 |
A minimal faithful permutation representation — 3 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)(33,35)(36,37,40,43)(38,44,47,51)(39,48,45,42)(41,49,50,46);(36,38,45,49,40,47,39,46)(37,41,48,51,43,50,42,44);(32,33,34,35)682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 175);