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) = C22×C4 |
| direct product | C13×#13232 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1964 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×#41 | C23×C13 |
| prime radical | C13×#535 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#131 ◁ G | |
448 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)(14,15,20,25,21,26,19,38)(16,27,31,34,32,42,30,45)(17,33,22,40,36,29,35,23)(18,24,28,41,37,44,39,43);(14,16,28,23)(15,22,41,34)(17,24,42,25)(18,29,20,31)(19,30,37,33)(21,32,39,40)(26,35,43,45)(27,38,36,44);(14,17,19,35,21,36,20,22)(15,23,25,33,26,40,38,29)(16,24,30,43,32,44,31,41)(18,34,28,42,37,45,39,27)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6220);