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×#3515 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
1014 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)(22,23,27,28)(24,25,29,32)(26,34,35,30)(31,37,36,33);(23,28)(25,32)(30,34)(33,37);(14,15)(16,19)(17,18)(20,21)(22,24,27,29)(23,25,28,32)(26,31,35,36)(30,33,34,37);(22,25)(23,29)(24,28)(26,33)(27,32)(30,36)(31,34)(35,37);(14,16,17,20)(15,19,18,21)(22,26)(23,30)(24,31)(25,33)(27,35)(28,34)(29,36)(32,37)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2247);