Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24×C42 |
| direct product | C13×#14274 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C13 | C24 |
| commutator | C23 | C23×C4×C13 |
| Frattini, cosocle | C24 | C24×C13 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
1742 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)(18,19,20,21)(27,31)(32,34)(33,39)(40,41);(22,23,24,25)(26,27,30,31)(28,34,36,32)(29,33,38,39)(35,41,37,40);(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,28,30,36)(27,32,31,34)(29,37,38,35)(33,41,39,40);(26,29,30,38)(27,33,31,39)(28,35,36,37)(32,40,34,41)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 7262);