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×#3556 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| prime radical | C23×C13 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
890 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,17)(16,22,24,20)(18,25,26,21)(23,27,29,28)(30,31,35,39)(32,37,33,36)(34,42,43,38)(40,44,41,45);(14,16,19,24)(15,20,17,22)(18,23,26,29)(21,27,25,28)(30,31)(32,37)(33,36)(34,38)(35,39)(40,45)(41,44)(42,43);(30,32,35,33)(31,36,39,37)(34,40,43,41)(38,44,42,45);(14,17,19,15)(16,20,24,22)(18,25,26,21)(23,27,29,28)(30,33,35,32)(31,37,39,36)(34,41,43,40)(38,45,42,44);(14,18,19,26)(15,21,17,25)(16,23,24,29)(20,27,22,28)(30,34,35,43)(31,38,39,42)(32,40,33,41)(36,44,37,45)494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2288);