Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#20886 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C22×C13 | C2×C4×D4 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C22×C13×M16 ◁ G | |
1326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,23,28,24,27,22,36)(20,29,32,25,31,40,37,41)(21,33,34,26,35,43,38,42)(30,39,47,48,45,49,46,44);(15,17)(18,20,23,32,24,31,22,37)(19,25,28,40,27,41,36,29)(21,30,34,47,35,45,38,46)(26,39,43,48,42,49,33,44);(18,21)(19,26)(20,30)(22,38)(23,34)(24,35)(25,39)(27,42)(28,43)(29,44)(31,45)(32,47)(33,36)(37,46)(40,48)(41,49);(19,27)(20,31)(26,42)(28,36)(30,45)(32,37)(33,43)(46,47)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13874);