Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#3547 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
1022 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(16,20)(22,23,26,27)(24,30,31,28)(25,33,34,29)(32,35,37,36);(15,18)(19,21)(23,27)(24,31)(29,33)(32,37);(14,15,17,18)(16,19,20,21)(22,24,26,31)(23,28,27,30)(25,32,34,37)(29,35,33,36);(14,16)(15,19)(17,20)(18,21)(22,23)(24,28)(25,29)(26,27)(30,31)(32,35)(33,34)(36,37);(22,25,26,34)(23,29,27,33)(24,32,31,37)(28,35,30,36)494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2279);