Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13011 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C2×D8 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | C4×D8 |
| prime radical | C2×C13×#508 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C22×C8×C13 ◁ C2×C4×C8×C13 ◁ G | |
476 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)(15,17)(18,19,24,31,25,32,22,29,26,33,42,48,34,43,23,30)(20,28,36,27,37,45,21,39,38,44,41,46,40,49,35,47);(14,15,16,17)(18,20,34,37,26,38,25,40)(19,27,43,39,33,46,32,47)(21,23,41,42,35,22,36,24)(28,29,45,31,44,30,49,48);(18,21)(19,28)(20,23)(22,38)(24,40)(25,36)(26,35)(27,29)(30,46)(31,39)(32,49)(33,44)(34,41)(37,42)(43,45)(47,48)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5999);