Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C25×C4 |
| direct product | C61×#13853 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C61 | C23 |
| commutator | C23 | C23×C4×C61 |
| Frattini, cosocle | C24 | C24×C61 |
| socle | C24×C61 | C24 |
| prime radical | C25×C61 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C61 ◁ G | |
1942 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2)(3,4)(5,6,7,8)(9,10)(11,14)(12,13)(15,16)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(10,13)(14,16)(17,18)(19,22)(20,21)(23,24);(2,4)(9,11,12,15)(10,14,13,16)(18,21)(22,24);(17,19,20,23)(18,22,21,24)5368 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 6841);