Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#22892 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×2−1+4 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
986 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)(14,15,17,16)(18,19,25,31)(20,32,21,35)(22,28,40,46)(23,30,24,29)(26,37,27,34)(33,48,36,44)(38,43,49,42)(39,47,41,45);(14,16,17,15)(18,20,25,21)(19,26,31,27)(22,38,40,49)(23,37,24,34)(28,44,46,48)(29,35,30,32)(33,41,36,39)(42,47,43,45);(18,21,25,20)(19,27,31,26)(22,36,40,33)(23,37,24,34)(28,43,46,42)(29,35,30,32)(38,39,49,41)(44,45,48,47);(18,22)(19,28)(20,33)(21,36)(23,41)(24,39)(25,40)(26,42)(27,43)(29,47)(30,45)(31,46)(32,48)(34,49)(35,44)(37,38)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 15880);