Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#8933 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #120 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | #385 |
| prime radical | C23×C13 | C22⋊Q8 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(16,19)(20,21)(22,23,26,31,28,25,27,30)(24,32,35,33,36,37,34,29);(14,15,17,18)(16,19,20,21)(22,24,27,34,28,36,26,35)(23,29,30,37,25,33,31,32);(14,16,17,20)(15,19,18,21)(22,25,28,23)(24,33,36,29)(26,30,27,31)(32,35,37,34)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1921);