Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#12660 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #117 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | #432 |
| prime radical | C23×C13 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#97 ◁ G | |
330 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)(14,15,16,17)(18,19)(20,28)(21,33)(22,27)(23,25)(24,30)(26,34)(29,37)(31,38)(32,41)(35,47)(36,39)(40,43)(42,45)(44,49)(46,48);(15,17)(18,20,21,31,22,32,35,46,23,30,34,45,36,29,43,44)(19,24,26,38,27,37,40,48,25,28,33,42,39,41,47,49);(19,25)(20,29,30,32)(21,34)(24,37,28,41)(27,39)(31,46,45,44)(35,43)(38,49,42,48)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5648);