Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#26271 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C2×#135×C61 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×C4×C61 ◁ G | |
752 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2)(3,7)(4,5)(6,8)(9,10)(11,22)(12,28)(13,31)(14,20)(15,21)(16,25)(17,24)(18,33)(19,32)(23,38)(26,36)(27,39)(29,35)(30,40)(34,37)(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);(2,5)(6,7)(9,11,14,25,15,27,32,26)(10,16,19,22,21,36,20,39)(12,13,24,33,30,34,29,23)(17,37,28,18,35,31,40,38);(9,12,14,24,15,30,32,29)(10,17,19,28,21,35,20,40)(11,23,25,13,27,33,26,34)(16,18,22,31,36,38,39,37);(1,3,4,8)(2,6,5,7)(9,13,32,23,15,34,14,33)(10,18,20,37,21,38,19,31)(11,24,26,12,27,29,25,30)(16,35,39,28,36,17,22,40)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 19259);