Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34745 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| socle | C23×C13 | C25 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
2522 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,22,25)(20,24,21,23)(26,27)(28,31)(29,30)(32,33);(14,15)(16,17)(18,20,22,21)(19,23,25,24);(15,17)(18,20,22,21)(19,24,25,23)(27,30)(31,33);(15,17)(18,21,22,20)(19,23,25,24);(26,28,29,32)(27,31,30,33)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27733);