Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#3509 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| prime radical | C2×C13×#41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
992 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(16,20)(18,21)(22,23,26,29)(24,27,32,30)(25,33,34,28)(31,36,37,35);(14,15,17,19)(16,18,20,21)(22,23)(24,30)(25,28)(26,29)(27,32)(31,36)(33,34)(35,37);(14,16,17,20)(15,18,19,21);(22,24)(23,27)(25,31)(26,32)(28,35)(29,30)(33,36)(34,37);(22,25,26,34)(23,28,29,33)(24,31,32,37)(27,35,30,36)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2241);