Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26251 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×C13×D8 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C4×C13×C4⋊C4 ◁ G | |
880 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)(20,24)(21,22)(23,25)(26,27)(28,34)(29,33)(30,37)(31,36)(32,38)(35,40)(39,41);(14,15)(16,17)(19,22)(23,24)(26,28,31,39,32,40,30,29)(27,33,37,35,38,41,36,34);(15,17)(26,29,30,40,32,39,31,28)(27,34,36,41,38,35,37,33);(18,20,21,25)(19,23,22,24)(26,29,30,40,32,39,31,28)(27,35,36,33,38,34,37,41)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19239);