Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C22 |
| direct product | C31×#472 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | #121 |
| commutator, Frattini, cosocle | C2×C4 | C23×C31 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C2×C4×C31 ◁ G | |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 496 |
A minimal faithful permutation representation — 3 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)(33,37)(34,41)(35,38)(40,45)(42,43)(44,46);(32,33,38,45,36,40,35,37)(34,39,41,46,43,47,42,44);(32,34)(33,39)(35,42)(36,43)(37,44)(38,41)(40,47)(45,46)496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 153);