Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#23730 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C23×C13 | C22×D4 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ C22×C42×C13 ◁ G | |
1126 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)(26,27,30,35,31,36,29,34)(28,37,38,33,40,41,39,32);(14,15)(16,17)(18,20,21,25)(19,22,23,24)(26,28)(27,32)(29,38)(30,39)(31,40)(33,36)(34,37)(35,41);(15,17)(26,28)(27,33)(29,38)(30,39)(31,40)(32,36)(34,41)(35,37);(26,29,31,30)(27,34,36,35)(28,38,40,39)(32,37,33,41)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16718);