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×#20521 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator | C22 | C22×C42×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle, prime radical | C23×C13 | C23×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
866 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19)(20,24)(21,25)(22,23)(26,27,31,34,30,33,39,29)(28,35,38,37,36,32,40,41);(14,15,17,16)(19,23)(24,25)(26,28,30,36)(27,32,33,35)(29,37,34,41)(31,38,39,40);(14,16,17,15)(18,20,22,21)(19,24,23,25)(27,33)(28,36)(29,34)(38,40);(18,21,22,20)(19,25,23,24)(26,29,39,33,30,34,31,27)(28,37,40,35,36,41,38,32)1300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13509);