Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34634 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| socle | C23×C13 | C25 |
| prime radical | C25×C13 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
2374 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,21,23)(20,24,25,22)(26,27)(28,31)(29,33)(30,32)(34,37)(35,38)(36,39)(40,41);(18,20,21,25)(19,22,23,24)(26,28)(27,31)(29,35)(30,34)(32,37)(33,38)(36,40)(39,41);(15,17)(28,34)(31,37)(35,40)(38,41);(27,32)(31,37)(33,39)(38,41);(26,29,30,36)(27,33,32,39)(28,35,34,40)(31,38,37,41)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27622);