Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#21027 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator | C23 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C23×C13 | C23×C4 |
| prime radical | C24×C13 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
906 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,23)(21,22)(24,25)(26,27,31,28,30,33,38,35)(29,32,37,34,36,39,41,40);(19,22)(23,25)(26,28,31,33,30,35,38,27)(29,34,37,39,36,40,41,32);(15,17)(18,20,21,24)(19,23,22,25)(26,29,30,36)(27,32,33,39)(28,34,35,40)(31,37,38,41);(27,33)(28,35)(29,36)(37,41)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14015);