Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C61 · Schur multiplier (H2) = C27×C4 |
| direct product | C61×#60826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C61 |
| prime radical | C61×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C4×#41×C61 ◁ G | |
2026 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 5 generators on 101 points:
(1,2)(3,7)(4,6)(5,8)(9,10,14,19)(11,15,20,28)(12,17,23,31)(13,16,25,18)(21,27,33,38)(22,29,34,26)(24,30,36,32)(35,39,40,37)(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);(1,3,4,8)(2,5,6,7)(9,11)(10,15)(12,21)(13,22)(14,20)(16,29)(17,27)(18,26)(19,28)(23,33)(24,35)(25,34)(30,39)(31,38)(32,37)(36,40);(3,8)(5,7)(10,16)(11,20)(13,25)(15,26)(17,30)(18,19)(21,33)(24,36)(27,37)(28,29)(31,32)(38,39);(2,6)(5,7)(9,12)(10,17)(11,21)(13,24)(14,23)(15,27)(16,30)(18,32)(19,31)(20,33)(22,35)(25,36)(26,37)(28,38)(29,39)(34,40);(12,23)(17,31)(21,33)(24,36)(27,38)(30,32)(35,40)(37,39)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 53814);