Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C31 · Schur multiplier (H2) = C23 |
| direct product | C31×#342 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | C22⋊C4 |
| commutator | C22 | C42×C31 |
| Frattini, cosocle | C24 | C22×C31 |
| prime radical | C24×C31 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C24×C31 ◁ G | |
142 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 496 |
A minimal faithful permutation representation — 2 generators on 43 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)(36,37)(38,42,43,40)(39,41);(32,33,34,35)(36,38)(37,40)(39,43)(41,42)682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 23);