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×#7048 |
| 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 | |
290 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 2 generators on 85 points:
(1,2)(3,5)(4,7)(6,8)(9,10,13,15,14,11,12,16)(18,22,23,24)(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);(2,5,7,6)(9,11,14,10)(12,15,13,16)(17,18,20,22,21,23,19,24)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 36);