Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#21003 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #121 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C22×C13 | C2×#121 |
| prime radical | C2×C13×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C4×C13 ◁ G | |
1686 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)(18,19,23,29,24,28,22,27)(20,25,31,39,32,41,33,40)(21,34,35,26,36,42,37,43)(30,44,46,38,47,48,45,49);(18,20,23,33,24,32,22,31)(19,25,27,39,28,41,29,40)(21,30,37,46,36,47,35,45)(26,38,42,44,43,49,34,48);(15,17)(18,21)(19,26)(20,30)(22,35)(23,37)(24,36)(25,38)(27,42)(28,43)(29,34)(31,45)(32,47)(33,46)(39,44)(40,48)(41,49);(18,22,24,23)(19,27,28,29)(20,31,32,33)(21,35,36,37)(25,39,41,40)(26,42,43,34)(30,45,47,46)(38,44,49,48)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13991);