Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C31 · Schur multiplier (H2) = C4 |
| direct product | C31×#433 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C31 | C23 |
| commutator | C22 | C22×C4×C31 |
| Frattini, cosocle | C2×C4 | C23×C31 |
| socle | C22×C31 | C22×C4 |
| prime radical | C23×C31 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C31 ◁ G | |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 3 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)(32,33)(34,37)(35,36)(38,39)(40,41,43,46,44,47,50,53)(42,45,49,52,48,51,54,55);(33,36)(37,39)(40,42)(41,45)(43,49)(44,48)(46,52)(47,51)(50,54)(53,55);(32,34,35,38)(33,37,36,39)(42,48)(45,51)(49,54)(52,55)868 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 114);