Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C2×C4 |
| direct product | C61×#10684 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C61 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C2×C42×C61 ◁ G | |
426 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,2,4,6)(3,7,8,5)(9,10,12,15,14,11,13,16)(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);(1,3,4,8)(2,5,6,7)(9,10)(11,14)(12,16)(13,15)(17,18,20,23)(19,21,24,22);(9,11,14,10)(12,15,13,16)(18,21)(19,24)(22,23)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 3672);