Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7035 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×#7041 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | #95 |
| commutator | C22×C4 | C42×C61 |
| Frattini, cosocle | C43 | C22×C61 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C43×C61 ◁ G | |
278 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 2 generators on 93 points:
(1,2,5,8)(3,6,7,4)(9,10,12,14,13,16,11,15)(17,18,20,25,22,26,21,24)(19,27,28,23,30,31,29,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3,6,2,5,7,4,8)(10,14)(11,12)(15,16)(17,19,21,29,22,30,20,28)(18,23,25,31,26,32,24,27)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 29);