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×#3524 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
1030 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)(19,21)(23,24)(26,34)(28,30)(32,37);(22,23,27,24)(25,30,33,28)(26,29,34,31)(32,36,37,35);(14,15)(16,19)(17,18)(20,21)(22,24,27,23)(25,30,33,28)(26,31,34,29)(32,36,37,35);(22,25,27,33)(23,28,24,30)(26,32,34,37)(29,35,31,36);(14,16,17,20)(15,19,18,21)(22,26)(23,29)(24,31)(25,32)(27,34)(28,35)(30,36)(33,37)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2256);