Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#26080 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C2×#41×C61 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×C4×C61 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2,4,6)(3,7,8,5)(9,10,14,20)(11,21,24,17)(12,25,27,39)(13,29,15,19)(16,30,32,23)(18,28,34,26)(22,36,38,31)(33,37,35,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(9,11,13,23,14,24,15,30)(10,16,19,21,20,32,29,17)(12,22,26,37,27,38,28,40)(18,31,25,35,34,36,39,33);(1,3,4,8)(2,5,6,7)(9,11,14,24)(10,17,20,21)(12,22,27,38)(13,23,15,30)(16,29,32,19)(18,33,34,35)(25,31,39,36)(26,37,28,40);(9,12,13,26,14,27,15,28)(10,18,19,25,20,34,29,39)(11,22,23,37,24,38,30,40)(16,31,21,35,32,36,17,33)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 19068);