Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13072 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #466 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
458 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,23,28,25,21,24,35)(20,29,32,46,33,45,41,47)(22,36,38,34,40,49,39,27)(26,42,43,31,30,48,44,37);(18,20,22,37,24,32,39,42,25,33,40,31,23,41,38,48)(19,26,34,29,28,44,49,47,21,30,27,45,35,43,36,46);(15,17)(18,21)(19,25)(20,30)(22,27)(23,28)(24,35)(26,33)(29,31)(32,43)(34,40)(36,39)(37,45)(38,49)(41,44)(42,46)(47,48)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6060);