Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C24 |
| direct product | C31×#563 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C31 |
| prime radical | C2×D4×C31 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ G | |
196 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 4 generators on 55 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)(33,36)(34,38)(40,41,45,43)(42,48,50,46)(44,51,53,47)(49,54,52,55);(33,36)(37,39)(40,42,45,50)(41,46,43,48)(44,52,53,49)(47,55,51,54);(32,33)(34,37)(35,36)(38,39)(40,43,45,41)(42,46,50,48)(44,51,53,47)(49,54,52,55);(32,34)(33,37)(35,38)(36,39)(40,44)(41,47)(42,49)(43,51)(45,53)(46,54)(48,55)(50,52)589 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 244);