Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26079 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C4×C13×C22⋊C4 ◁ G | |
782 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,21,23)(20,24,25,22)(26,27)(28,33)(29,39)(30,40)(31,35)(32,38)(34,36)(37,41);(14,15)(16,17)(26,28,36,29,31,37,30,38)(27,32,40,41,35,39,34,33);(15,17)(18,20,21,25)(19,22,23,24)(28,37)(29,38)(32,39)(33,41);(26,29,36,37,31,38,30,28)(27,33,40,32,35,41,34,39)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19067);