Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#15535 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C13 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
1082 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)(15,17)(18,19)(20,23)(21,22)(24,25)(26,27,29,31)(28,30,32,33)(34,35,38,40)(36,37,41,39);(19,21)(20,24)(28,32)(30,33)(34,36,38,41)(35,39,40,37);(18,20,22,24)(19,23,21,25)(26,28)(27,30)(29,32)(31,33)(34,36)(35,39)(37,40)(38,41);(14,15)(16,17)(18,21,22,19)(20,25,24,23)(26,27)(28,30)(29,31)(32,33)(34,37,38,39)(35,36,40,41)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 8523);