Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7734 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×#7766 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C61 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C2×C42×C61 ◁ G | |
436 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,2,4,7)(3,5,8,6)(13,16)(18,21)(19,23)(22,24)(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);(2,5)(3,8)(6,7)(9,10,12,14)(11,13,15,16);(9,11)(10,13)(12,15)(14,16)(17,18,20,22)(19,24,23,21)2257 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 754);