Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C23 |
| direct product | C2×C31×D16 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | D8 |
| commutator, Frattini, cosocle | C8 | C23×C31 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C2×C4×C31 ◁ C2×C8×C31 ◁ G | |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49);(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18);(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 186);