Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C23 |
| direct product | C31×#454 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | #120 |
| commutator, Frattini, cosocle | C2×C4 | C23×C31 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C2×C4×C31 ◁ G | |
146 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)(35,42)(38,46)(39,43)(40,44)(45,47);(32,33)(34,38)(35,43)(36,39)(37,42)(40,45)(41,47)(44,46);(32,34,36,41)(33,38,39,47)(35,44,42,40)(37,45,43,46)496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 135);