Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34350 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| socle | C23×C13 | C25 |
| prime radical | C2×C13×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
2106 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
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)(20,24)(21,22)(23,25)(26,27)(28,34)(29,33)(30,32)(31,35)(36,40)(37,39)(38,41);(18,19)(20,23)(21,22)(24,25)(26,28)(27,31)(29,36)(30,35)(32,34)(33,38)(37,41)(39,40);(19,22)(23,24)(28,35)(31,34)(36,41)(38,40);(18,20,21,25)(19,23,22,24)(27,32)(28,35)(33,39)(36,41);(26,29,30,37)(27,33,32,39)(28,36,35,41)(31,38,34,40)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27338);