Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33469 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33471 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#442 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#509 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
668 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,25,29,42)(17,31)(18,22)(19,32)(20,24)(21,28,38,45)(23,33)(26,43,37,34)(27,41,30,39)(35,36)(40,44);(14,16)(15,21)(17,26)(18,27)(19,34)(20,29)(22,37)(23,39)(24,38)(25,35)(28,44)(30,31)(32,42)(33,45)(36,43)(40,41);(14,17,31,15,20,22,18,24)(16,26,30,21,29,37,27,38)(19,35,44,40,36,32,33,23)(25,28,41,43,42,45,39,34);(14,18,20,31)(15,22,24,17)(16,27,29,30)(19,33,36,44)(21,37,38,26)(23,35,40,32)(25,41,42,39)(28,34,45,43)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26459);