Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34491 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
1956 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(19,22)(20,21)(27,31)(29,37)(32,34)(35,41);(18,19,23,22)(20,25,21,24)(26,27)(28,34)(29,33)(30,31)(32,36)(35,40)(37,38)(39,41);(18,20,23,21)(19,24,22,25);(14,16,17,15)(18,21,23,20)(19,25,22,24)(26,28,30,36)(27,32,31,34)(29,35,37,41)(33,39,38,40);(18,22,23,19)(20,25,21,24)(26,29,30,37)(27,33,31,38)(28,35,36,41)(32,39,34,40)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27479);