Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C24 |
| direct product | C31×#556 |
| 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 | |
212 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 4 generators on 47 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)(32,33)(34,36)(35,38)(37,39)(42,46)(44,47);(32,34,37,35)(33,38,39,36)(40,41,43,45)(42,44,46,47);(32,35,37,34)(33,38,39,36)(40,42)(41,44)(43,46)(45,47);(32,36,37,38)(33,34,39,35)775 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 237);