Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#32938 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#2615 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C22×C13×#41 ◁ G | |
1436 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,21)(23,27)(25,33)(28,34)(29,35)(30,37)(32,36);(22,23,25,27,26,29,33,35)(24,30,32,37,31,28,36,34);(15,17)(22,24)(23,28)(25,32)(26,31)(27,34)(29,30)(33,36)(35,37);(19,21)(24,31)(28,30)(32,36)(34,37)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25926);