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×#3516 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
1012 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)(23,26)(24,30)(29,33)(31,36);(22,23,27,26)(24,28,30,32)(25,33,34,29)(31,37,36,35);(14,15)(16,19)(17,18)(20,21)(22,24)(23,28)(25,31)(26,32)(27,30)(29,35)(33,37)(34,36);(22,25,27,34)(23,29,26,33)(24,31,30,36)(28,35,32,37);(14,16,17,20)(15,19,18,21)(22,26,27,23)(24,32,30,28)(25,33,34,29)(31,37,36,35)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2248);