Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13026 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#97 ◁ G | |
486 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)(18,19,22,27,37,46,38,47,24,29,21,26,23,28,39,48)(20,30,32,42,40,45,35,25,34,41,31,49,33,44,36,43);(14,15,16,17)(18,20)(19,25)(21,35)(22,36)(23,40)(24,34)(26,44)(27,45)(28,49)(29,43)(30,47)(31,38)(32,39)(33,37)(41,48)(42,46);(18,20)(19,25)(21,36)(22,35)(23,40)(24,34)(26,45)(27,44)(28,49)(29,43)(30,48)(31,39)(32,38)(33,37)(41,47)(42,46)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6014);