Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#2810 |
| 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)(16,20)(17,18)(19,21)(23,26)(24,28)(30,31,35,32)(33,37,34,36);(15,18)(16,21)(22,23,25,26)(24,29,28,27)(30,32,35,31)(33,37,34,36);(14,16)(15,19)(17,21)(18,20)(30,33,35,34)(31,36,32,37);(14,15)(16,19)(17,18)(20,21)(22,24,25,28)(23,27,26,29)(30,34,35,33)(31,37,32,36)416 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 1542);