Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8790 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C2×C8 |
| direct product | C61×#8793 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #382 |
| commutator | C42 | C22×C4×C61 |
| Frattini, cosocle | C2×C42 | C23×C61 |
| prime radical | C23×C61 | #124 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 3 generators on 101 points:
(2,3)(4,5)(7,8)(9,10)(11,19,23,15)(12,24,26,39)(13,18)(14,17)(16,25,30,34)(20,27)(21,35)(22,32,33,29)(28,36)(31,40)(37,38)(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);(1,2,4,3,6,8,5,7)(9,11,20,33,14,23,13,22)(10,15,27,32,17,19,18,29)(12,21,34,40,26,37,25,36)(16,28,39,35,30,31,24,38);(1,3,5,2,6,7,4,8)(9,12,14,26)(10,16)(11,21,23,37)(13,25,20,34)(15,28)(17,30)(18,24)(19,31)(22,36,33,40)(27,39)(29,38)(32,35)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1781);