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×#554 |
| 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 | |
228 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 166 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)(32,33,36,35)(34,38,39,37)(40,41,44,43)(42,46,47,45);(33,35)(37,38)(40,42,44,47)(41,45,43,46);(32,34)(33,37)(35,38)(36,39);(32,35,36,33)(34,38,39,37)(40,43,44,41)(42,45,47,46)775 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 235);