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×#3564 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| prime radical | C13×#538 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
936 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)(14,15,19,23)(16,24,25,21)(17,28,31,22)(18,20,30,34)(26,36,38,37)(27,35,39,32)(29,42,43,33)(40,45,41,44);(15,20)(16,25)(17,29)(21,35)(23,34)(24,32)(26,40)(27,39)(31,43)(36,37)(38,41)(44,45);(14,16,18,27)(15,21,20,32)(17,26,29,41)(19,25,30,39)(22,36,33,44)(23,24,34,35)(28,37,42,45)(31,38,43,40);(14,17,30,43)(15,22,34,42)(16,26,39,40)(18,29,19,31)(20,33,23,28)(21,36,35,45)(24,37,32,44)(25,38,27,41);(15,20)(21,32)(22,33)(23,34)(24,35)(28,42)(36,44)(37,45)494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2296);