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×#3495 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| prime radical | C13×#525 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
1022 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 416 |
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)(22,23,27,30)(24,25,32,28)(26,34,35,29)(31,36,37,33);(14,15,17,19)(16,18,20,21)(22,24,27,32)(23,28,30,25)(26,31,35,37)(29,36,34,33);(14,16)(15,18)(17,20)(19,21)(22,25)(23,24)(26,33)(27,28)(29,31)(30,32)(34,37)(35,36);(22,24)(23,25)(26,31)(27,32)(28,30)(29,33)(34,36)(35,37);(22,26,27,35)(23,29,30,34)(24,31,32,37)(25,33,28,36)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2227);