Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C61 · Schur multiplier (H2) = C28 |
| direct product | C61×#60939 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C61 |
| prime radical | C61×#3054 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×#117×C61 ◁ G | |
1758 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)(9,10,14,18)(11,19,20,32)(12,16,23,30)(13,25,27,17)(15,26,28,22)(21,33,34,40)(24,37,36,31)(29,38,39,35)(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)(11,20)(15,28)(19,32)(21,34)(22,26)(29,39)(33,40)(35,38);(2,5)(6,8)(9,11,14,20)(10,15,18,28)(12,21,23,34)(13,26,27,22)(16,29,30,39)(17,32,25,19)(24,38,36,35)(31,40,37,33);(1,3,4,7)(2,6,5,8)(9,12)(10,16)(11,21)(13,24)(14,23)(15,29)(17,31)(18,30)(19,33)(20,34)(22,35)(25,37)(26,38)(27,36)(28,39)(32,40);(12,23)(16,30)(21,34)(24,36)(29,39)(31,37)(33,40)(35,38)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 53927);