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×#356 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | #99 |
| commutator | C2×C4 | C2×C4×C31 |
| Frattini, cosocle | C2×Q8 | C22×C31 |
| prime radical | C22×C31 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C22×C31 ◁ C2×Q8×C31 ◁ G | |
60 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)(32,33,36,40,37,41,34,42)(35,39,43,46,45,47,44,38);(32,34,37,36)(33,38,41,46)(35,44,45,43)(39,40,47,42)403 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 37);