Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9758 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C2×C4 |
| direct product | C61×#9765 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #390 |
| commutator | C42 | C22×C4×C61 |
| Frattini, cosocle | C2×C42 | C23×C61 |
| prime radical | C23×C61 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
374 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 3 generators on 109 points:
(1,2,5,8,6,9,4,14)(3,10,13,15,11,16,12,7)(17,18)(19,28,31,39)(20,32)(21,26)(22,37)(23,27)(24,30,40,36)(25,34)(29,38,44,48)(33,41)(35,46)(42,47,45,43)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(1,3,6,11)(2,7)(4,12,5,13)(8,10)(9,15)(14,16)(17,19,21,36,23,31,22,30)(18,24,26,39,27,40,37,28)(20,29,33,47,35,44,34,43)(25,38,32,45,41,48,46,42);(3,11)(7,15)(10,16)(12,13)(17,20,22,34,23,35,21,33)(18,25,26,32,27,41,37,46)(19,29,30,43,31,44,36,47)(24,38,39,45,40,48,28,42)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 2753);