Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#2769 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C13 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
344 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,16)(17,20,21,19)(22,23)(24,27)(25,26)(28,29)(32,35)(33,37);(15,16)(17,21)(23,25)(27,28)(30,31,34,36)(32,33,35,37);(14,16,18,15)(17,20,21,19)(22,24,26,29)(23,27,25,28)(30,32,34,35)(31,33,36,37);(14,17,18,21)(15,19,16,20)(22,25,26,23)(24,28,29,27)(30,33)(31,35)(32,36)(34,37)416 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 1501);