Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C22 |
| direct product | C31×#510 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | C2×D8 |
| commutator, Frattini, cosocle | C8 | C23×C31 |
| prime radical | C31×#135 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C2×C8×C31 ◁ G | |
82 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)(34,42)(35,46)(36,51)(37,39)(38,43)(40,49)(41,48)(44,62)(45,59)(47,57)(50,58)(52,56)(53,61)(54,63)(55,60);(32,34,37,45)(33,38,39,53)(35,47,50,63)(36,52,48,44)(40,56,55,62)(41,57,51,54)(42,58,59,46)(43,60,61,49);(33,39)(38,53)(40,55)(41,51)(42,59)(46,58)(54,57)(56,62)496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 191);