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×#3512 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
1032 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)(16,20)(18,21)(22,23)(24,29)(25,30)(26,34)(27,28)(31,35)(32,33)(36,37);(14,15,17,19)(16,18,20,21)(23,28)(25,29)(31,34)(33,36);(14,16,17,20)(15,18,19,21)(22,24,27,30)(23,29,28,25)(26,32,35,37)(31,36,34,33);(22,25,27,29)(23,30,28,24)(26,33,35,36)(31,37,34,32);(22,26,27,35)(23,31,28,34)(24,32,30,37)(25,33,29,36)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2244);