Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#13245 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #466 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C22×C13×D16 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
442 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)(15,17)(18,19,24,30,26,31,25,34)(20,32,35,42,28,22,29,23)(21,36,39,33,41,48,40,44)(27,43,45,49,46,37,47,38);(14,15,16,17)(18,20,32,34,25,35,23,19,26,28,22,30,24,29,42,31)(21,33,43,47,40,48,38,27,41,44,37,45,39,36,49,46);(18,21,22,37,25,40,42,49,26,41,32,43,24,39,23,38)(19,27,20,33,30,45,35,48,31,46,28,44,34,47,29,36)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6233);