Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #353 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C31 · Schur multiplier (H2) = C2 |
| direct product | C31×#355 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | #99 |
| commutator | C2×C4 | C2×C4×C31 |
| Frattini, cosocle | C2×Q8 | C22×C31 |
| prime radical | C2×D4×C31 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C22×C31 ◁ C2×Q8×C31 ◁ G | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 496 |
A minimal faithful permutation representation — 2 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)(32,33,35,39,36,40,44,47)(34,38,42,46,41,37,43,45);(33,37)(34,41)(38,40)(39,46)(42,43)(45,47)403 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 36);