Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#19801 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C61 |
| prime radical | C61×#550 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C42×C61 ◁ G | |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 93 points:
(2,7)(3,5)(8,15)(9,13)(10,14)(11,16)(17,18,21,25)(19,22,27,31)(20,23,28,24)(26,29,32,30)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,2,6,9)(3,7,5,13)(4,11,12,15)(8,14,16,10)(17,19,21,27)(18,22,25,31)(20,26,28,32)(23,29,24,30);(1,3,6,5)(2,7,9,13)(4,10,12,14)(8,15,16,11)(18,23)(20,28)(22,29)(24,25)(26,32)(30,31);(1,4,6,12)(2,8,9,16)(3,10,5,14)(7,15,13,11)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 12789);