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×#3491 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| prime radical | C13×#534 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
1052 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)(24,28)(25,32)(26,27)(29,33)(30,36)(31,34)(35,37);(14,15,17,19)(16,18,20,21)(23,27)(28,34)(29,32)(35,36);(14,16)(15,18)(17,20)(19,21)(22,24,26,31)(23,28,27,34)(25,30,33,37)(29,35,32,36);(22,23)(24,28)(25,29)(26,27)(30,35)(31,34)(32,33)(36,37);(22,25)(23,29)(24,30)(26,33)(27,32)(28,35)(31,37)(34,36)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2223);