Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#23601 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C22×C13 | C2×#121 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C4×C13 ◁ G | |
994 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)(18,19,22,27,24,28,23,37)(20,29,31,40,33,46,32,25)(21,26,38,43,36,44,35,42)(30,45,48,39,47,41,34,49);(14,15)(16,17)(18,20,23,32,24,33,22,31)(19,25,27,29,28,40,37,46)(21,34,35,47,36,48,38,30)(26,41,43,49,44,45,42,39);(15,17)(18,21)(19,26)(20,30)(22,35)(23,38)(24,36)(25,39)(27,42)(28,44)(29,45)(31,34)(32,48)(33,47)(37,43)(40,49)(41,46);(18,22,24,23)(19,27,28,37)(20,31,33,32)(21,35,36,38)(25,29,40,46)(26,42,44,43)(30,34,47,48)(39,45,49,41)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16589);