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×#3554 |
| 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)(14,15)(16,20)(17,18)(19,21)(23,27)(24,30)(25,33)(35,37);(15,18)(19,20)(22,23,26,27)(24,31,30,28)(25,29,33,34)(32,37,36,35);(22,24,26,30)(23,28,27,31)(25,32,33,36)(29,35,34,37);(14,15)(16,19)(17,18)(20,21)(22,23)(24,28)(25,29)(26,27)(30,31)(32,35)(33,34)(36,37);(14,16,17,21)(15,19,18,20)(22,25,26,33)(23,29,27,34)(24,32,30,36)(28,35,31,37)494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2286);