Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26171 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C4×C13×C4⋊C4 ◁ G | |
800 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)(20,23)(21,25)(22,24)(26,27,31,35)(28,34,30,32)(29,37,38,41)(33,39,40,36);(14,15)(16,17)(18,20,22,21)(19,23,24,25)(27,32)(28,30)(33,37)(34,35)(36,39)(40,41);(15,17)(18,21,22,20)(19,23,24,25)(26,28,31,30)(27,32,35,34)(29,36,38,39)(33,37,40,41);(26,29,31,38)(27,33,35,40)(28,36,30,39)(32,37,34,41)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19159);