Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C61 · Schur multiplier (H2) = C28 |
| direct product | C61×#60927 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C61 |
| prime radical | C61×#3062 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C4×#41×C61 ◁ G | |
1772 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 5 generators on 101 points:
(2,5)(3,7)(9,10)(11,19)(12,23)(13,17)(14,28)(15,21)(16,26)(18,27)(20,36)(22,31)(24,40)(25,34)(29,33)(30,39)(32,37)(35,38)(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)(3,6)(4,5)(7,8)(9,11)(10,15)(12,24)(13,21)(14,22)(16,32)(17,19)(18,31)(20,25)(23,36)(26,39)(27,38)(28,35)(29,37)(30,33)(34,40);(2,5)(6,8)(9,12,13,25)(10,16,17,33)(11,20,21,24)(14,29,27,26)(15,30,19,32)(18,34,28,23)(22,39,38,37)(31,36,35,40);(1,3,4,7)(2,6,5,8)(10,17)(15,19)(16,33)(18,28)(23,34)(30,32)(31,35)(36,40);(11,21)(15,19)(20,24)(22,38)(30,32)(31,35)(36,40)(37,39)2989 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 53915);