Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#23717 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C61 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| socle | C22×C61 | C2×#121 |
| prime radical | C2×#41×C61 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C61 ◁ C2×C42×C61 ◁ G | |
752 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2)(3,6)(4,5)(7,8)(9,10,13,18,15,20,14,19)(11,16,22,31,23,32,29,36)(12,24,26,35,28,34,27,17)(21,33,25,39,37,40,38,30)(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);(2,5)(6,8)(9,11)(10,16)(12,25)(13,22)(14,29)(15,23)(17,33)(18,31)(19,36)(20,32)(21,27)(24,39)(26,37)(28,38)(30,34)(35,40);(9,12,15,28)(10,17,20,35)(11,21,23,37)(13,27,14,26)(16,30,32,39)(18,34,19,24)(22,38,29,25)(31,40,36,33);(1,3,4,7)(2,6,5,8)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 16705);