Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24468 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24×C4 |
| direct product | C61×#25596 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C61×#535 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
1064 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)(9,10,13,17)(11,19,21,15)(12,16,24,32)(14,27,26,18)(20,29,36,35)(22,30,28,34)(23,37,38,31)(25,40,39,33)(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)(10,15)(12,23)(13,21)(14,28)(16,31)(17,19)(18,34)(20,25)(22,26)(24,38)(27,30)(29,33)(32,37)(35,40)(36,39);(9,12)(10,16)(11,20,21,36)(13,24)(14,25)(15,29,19,35)(17,32)(18,33)(22,23,28,38)(26,39)(27,40)(30,31,34,37);(1,3,4,8)(2,6,5,7)(10,17)(12,24)(15,19)(18,27)(20,36)(23,38)(25,39)(30,34)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 18584);