Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13073 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #466 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
478 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)(14,15)(16,17)(18,19,23,28,25,21,24,36)(20,29,33,46,34,45,41,47)(22,37,39,35,30,48,40,27)(26,42,43,32,31,49,44,38);(18,20,30,32,24,33,39,49,25,34,22,38,23,41,40,42)(19,26,27,45,28,44,37,46,21,31,35,29,36,43,48,47);(15,17)(18,21)(19,25)(20,31)(22,27)(23,28)(24,36)(26,34)(29,32)(30,35)(33,43)(37,40)(38,45)(39,48)(41,44)(42,46)(47,49)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6061);