Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C24 |
| direct product | C8×C13×#125 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C13 | C23 |
| commutator | C22 | C23×C8×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle, prime radical | C23×C13 | C23×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C13 ◁ G | |
742 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8)(25,26,27,28,29,30,31,32,33,34,35,36,37);(11,15)(13,16)(17,18,20,22)(19,21,23,24);(9,10,12,14)(11,13,15,16)(17,18)(19,21)(20,22)(23,24);(9,11)(10,13)(12,15)(14,16)(17,19,20,23)(18,21,22,24)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14660);