Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13229 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C42 |
| direct product | C13×#13231 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1964 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×#41 | C23×C13 |
| prime radical | C13×#3058 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#131 ◁ G | |
468 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,18,26,33)(17,27)(19,34)(20,23)(21,30)(22,28)(24,36,39,45)(25,40,37,32)(29,43,44,38)(31,41)(35,42);(14,16,18,23,20,26,33,15)(17,24,29,35,31,39,44,21)(19,25,32,34,28,37,40,22)(27,30,38,36,41,42,43,45);(14,17,28,42,20,31,19,30)(15,21,34,41,23,35,22,27)(16,24,37,43,26,39,25,38)(18,29,40,45,33,44,32,36)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6219);