Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C61 · Schur multiplier (H2) = C28 |
| direct product | C61×#60921 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C61 |
| prime radical | C61×#3455 | 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)(11,15)(12,22)(13,25)(14,17)(16,23)(18,27)(19,33)(20,29)(21,37)(24,32)(26,31)(28,35)(30,36)(34,40)(38,39)(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)(9,11,14,20)(10,15,17,29)(12,19,24,34)(13,21,27,36)(16,28,31,39)(18,30,25,37)(22,33,32,40)(23,35,26,38);(2,5)(6,8)(9,12,14,24)(10,16,17,31)(11,19,20,34)(13,26,27,23)(15,28,29,39)(18,32,25,22)(21,38,36,35)(30,40,37,33);(1,3,4,7)(2,6,5,8)(11,20)(15,29)(19,34)(21,36)(28,39)(30,37)(33,40)(35,38);(10,17)(15,29)(16,31)(18,25)(22,32)(28,39)(30,37)(33,40)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 53909);