Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C25 |
| direct product | C31×#575 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C31 | C2×D4 |
| commutator, Frattini, cosocle | C4 | C24×C31 |
| socle | C2×C31 | C22×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C31 ◁ C22×C4×C31 ◁ G | |
262 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 158 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) = 496 |
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)(34,41)(35,40)(36,44)(37,39)(38,42)(43,47)(45,46);(32,34)(33,38)(35,42)(36,45)(37,43)(39,46)(40,47)(41,44);(33,39)(38,46)(40,44)(41,47);(32,35,37,36)(33,40,39,44)(34,42,43,45)(38,47,46,41)682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 256);