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×#473 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | #121 |
| commutator, Frattini, cosocle | C2×C4 | C23×C31 |
| prime radical | #41×C31 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C2×C4×C31 ◁ G | |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 3 generators on 63 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)(32,33,38,43)(34,44,48,54)(35,49,51,57)(36,42,37,41)(39,47,55,46)(40,52,56,50)(45,59,61,53)(58,62,63,60);(32,34,37,47,38,48,36,46)(33,39,42,54,43,55,41,44)(35,45,52,62,51,61,50,60)(40,53,57,63,56,59,49,58);(32,35)(33,40)(34,45)(36,50)(37,52)(38,51)(39,53)(41,49)(42,57)(43,56)(44,58)(46,60)(47,62)(48,61)(54,63)(55,59)496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 154);