Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×C4⋊#401 |
| unambiguous semidirect product | C4⋊(C13×#401) |
| 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 | |
1106 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)(19,21)(23,24)(26,27,31,29)(28,33,30,32)(34,35,38,41)(36,39,40,37);(18,19,22,21)(20,24,25,23)(26,28,31,30)(27,32,29,33)(34,36,38,40)(35,39,41,37);(18,20,22,25)(19,23,21,24)(26,29,31,27)(28,33,30,32)(34,35)(36,39)(37,40)(38,41);(14,15,16,17)(18,21,22,19)(20,24,25,23)(26,30,31,28)(27,33,29,32)(34,37,38,39)(35,40,41,36)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 8142);