Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C25 |
| direct product | D4×Q8×C31 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C31 |
| prime radical | C2×D4×C31 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ G | |
280 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4)(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);(2,4);(5,6,7,8)(9,12,11,10);(5,9,7,11)(6,10,8,12)775 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 230);