Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#22109 |
| 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 | |
728 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)(19,22)(20,24)(26,27,32,28,31,34,30,36)(29,33,37,35,38,41,39,40);(18,19)(20,23)(21,22)(24,25)(26,28,32,34,31,36,30,27)(29,35,37,41,38,40,39,33);(15,17)(19,22)(23,25)(26,29)(27,33)(28,35)(30,39)(31,38)(32,37)(34,41)(36,40);(18,20,21,24)(19,23,22,25)(26,30,31,32)(27,28,34,36)(29,37,38,39)(33,40,41,35)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 15097);