Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#22690 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
846 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)(20,32)(21,36)(22,28)(23,30)(24,29)(25,31)(26,34)(27,37)(33,47)(35,45)(38,46)(39,49)(40,43)(41,44)(42,48);(18,20,25,35)(19,26,31,44)(21,22,38,40)(23,41,24,34)(27,43,47,28)(29,45,30,32)(33,42,37,39)(36,49,46,48);(18,21,24,37,25,38,23,33)(19,27,30,36,31,47,29,46)(20,22,34,39,35,40,41,42)(26,43,32,49,44,28,45,48);(18,22)(19,28)(20,33)(21,34)(23,42)(24,39)(25,40)(26,36)(27,45)(29,49)(30,48)(31,43)(32,47)(35,37)(38,41)(44,46)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 15678);