Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#2658 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C13 |
| prime radical | C22×D4×C13 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
612 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(23,27)(24,30)(29,35)(32,33);(18,19,20,21)(22,23)(24,31)(25,29)(26,27)(28,30)(32,37)(33,36)(34,35);(14,15)(16,17)(18,19)(20,21)(22,24)(23,28)(25,33)(26,30)(27,31)(29,37)(32,34)(35,36);(22,25,26,34)(23,29,27,35)(24,32,30,33)(28,36,31,37)416 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 1390);