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×#26990 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C61×#537 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×C4×C61 ◁ G | |
766 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)(4,6)(5,8)(9,10)(11,17)(12,25)(13,28)(14,21)(15,20)(16,23)(18,29)(19,26)(22,36)(24,32)(27,31)(30,35)(33,37)(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);(1,3,4,8)(2,5,6,7)(9,11,14,23,15,12,26,24)(10,16,19,17,20,32,21,25)(13,22,29,37,30,27,40,38)(18,31,28,33,34,36,35,39);(2,6)(5,7)(9,12)(10,17)(11,15)(13,27)(14,24)(16,21)(18,33)(19,32)(20,25)(22,30)(23,26)(28,36)(29,38)(31,35)(34,39)(37,40);(2,6)(5,7)(9,13,26,40,15,30,14,29)(10,18,21,35,20,34,19,28)(11,22,24,38,12,27,23,37)(16,31,25,39,32,36,17,33)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 19978);