Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13313 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13470 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #466 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C22×C13×D8 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,24,41,25,31,39,30)(20,32,37,44,38,48,49,46)(21,27,33,28,22,29,23,40)(26,42,47,34,43,36,45,35);(14,15)(16,17)(18,20,33,42,24,37,22,34,25,38,23,36,39,49,21,35)(19,26,27,46,30,45,40,48,31,43,29,44,41,47,28,32);(15,17)(19,27)(20,34)(21,33)(22,23)(24,39)(26,43)(28,30)(29,31)(32,44)(35,38)(36,49)(37,42)(40,41)(46,48)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6458);