Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18425 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3536 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
994 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)(14,15,20,17)(16,26,30,40)(18,24,19,32)(21,25,37,33)(22,35,27,28)(23,36,31,34)(29,42,44,38)(39,45,43,41);(14,16,20,30)(15,22,17,27)(18,28,19,35)(21,29,37,44)(23,38,31,42)(24,40,32,26)(25,39,33,43)(34,41,36,45);(14,17,20,15)(16,27,30,22)(18,23,19,31)(21,33,37,25)(24,36,32,34)(26,41,40,45)(28,38,35,42)(29,43,44,39);(14,18,20,19)(15,23,17,31)(16,28,30,35)(21,34,37,36)(22,38,27,42)(24,33,32,25)(26,39,40,43)(29,41,44,45)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11413);