Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C13 · Schur multiplier (H2) = C25×C42 |
| direct product | C13×#13756 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C13 | C23 |
| commutator | C22 | C22×C42×C13 |
| Frattini, cosocle | C24 | C24×C13 |
| socle | C24×C13 | C24 |
| prime radical | C25×C13 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C13 ◁ G | |
3070 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,20,21)(26,27)(28,31)(29,30)(32,33);(15,17)(22,23,24,25);(27,30)(31,33);(26,28,29,32)(27,31,30,33)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6744);