Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C22×C13×#366 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C13 | D8 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ C23×C4×C13 ◁ C23×C8×C13 ◁ G | |
782 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2)(25,26,27,28,29,30,31,32,33,34,35,36,37);(3,4);(5,6,7,8)(10,14)(11,15)(12,18)(16,24)(17,22)(19,23)(20,21);(9,10,15,21,12,16,19,22,13,17,23,24,18,20,11,14)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26393);