Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#22737 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator | C23 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle, prime radical | C23×C13 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
712 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(19,23)(24,25)(26,27,29,33,30,32,36,39)(28,31,35,38,34,37,40,41);(18,19,22,23)(20,24,21,25)(26,28)(27,31)(29,35)(30,34)(32,37)(33,38)(36,40)(39,41);(14,15,16,17)(18,20,22,21)(19,24,23,25)(28,34)(31,37)(35,40)(38,41);(18,21,22,20)(19,24,23,25)(27,32)(31,37)(33,39)(38,41)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 15725);