Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#10817 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #117 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C22×C13 | #382 |
| prime radical | C24×C13 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#117 ◁ G | |
642 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,30,33,25)(21,35,37,43)(22,28)(23,29)(24,27)(26,36,42,38)(31,45)(32,41,34,40)(39,46)(44,47)(48,49);(18,20,23,34,24,33,22,32)(19,25,29,41,27,30,28,40)(21,31,38,47,37,48,36,46)(26,39,43,45,42,44,35,49);(15,17)(18,21)(19,26,27,42)(20,31)(22,36)(23,38)(24,37)(25,39,30,44)(28,35,29,43)(32,46)(33,48)(34,47)(40,49,41,45)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3805);