Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#21071 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C22×C13 | C2×C4×D4 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C22×C13×M16 ◁ G | |
1050 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16)(18,19,22,26,23,21,30,25)(20,24,29,32,28,27,33,31);(14,15,17,16)(18,20,22,29,23,28,30,33)(19,24,26,32,21,27,25,31);(14,16,17,15)(18,21)(19,23)(20,27)(22,25)(24,28)(26,30)(29,31)(32,33);(20,28)(24,27)(29,33)(31,32)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14059);