Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#36711 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| prime radical | C23×D4×C13 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
2422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(20,24)(23,25)(26,27,32,35)(28,30,29,33)(31,39,40,34)(36,41,37,38);(19,22)(23,25)(26,28,32,29)(27,33,35,30)(31,36,40,37)(34,41,39,38);(14,15)(16,17)(18,19)(20,23)(21,22)(24,25)(26,29,32,28)(27,33,35,30)(31,37,40,36)(34,41,39,38);(18,19)(20,23)(21,22)(24,25)(26,30,32,33)(27,28,35,29)(31,38,40,41)(34,36,39,37);(18,20)(19,23)(21,24)(22,25)(26,31)(27,34)(28,36)(29,37)(30,38)(32,40)(33,41)(35,39)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29699);