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×#3568 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
958 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,21)(16,25,29,27)(17,20,24,30)(18,32,33,23)(22,36,35,26)(28,41,42,39)(31,43,38,34)(37,40,44,45);(15,21)(16,26)(17,24)(22,27)(23,32)(25,35)(28,40)(29,36)(31,38)(37,41)(39,44)(42,45);(14,16,19,29)(15,22,21,35)(17,27,24,25)(18,28,33,42)(20,26,30,36)(23,37,32,44)(31,41,38,39)(34,40,43,45);(14,17,30,15)(16,27,36,22)(18,31,43,23)(19,24,20,21)(25,26,35,29)(28,41,45,37)(32,33,38,34)(39,40,44,42);(14,18,30,43)(15,23,17,31)(16,28,36,45)(19,33,20,34)(21,32,24,38)(22,37,27,41)(25,39,35,44)(26,40,29,42)494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2300);