Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#20553 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator | C22 | C22×C42×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C23×C13 | C23×C4 |
| prime radical | C24×C13 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
870 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)(26,27,30,34,32,35,31,28)(29,33,39,37,38,41,40,36);(19,22)(20,24)(26,28,31,35,32,34,30,27)(29,37,40,33,38,36,39,41);(18,20,21,24)(19,23,22,25)(26,29)(27,33)(28,36)(30,39)(31,40)(32,38)(34,37)(35,41);(19,22)(23,25)(29,38)(33,41)(36,37)(39,40)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13541);