Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#33686 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C61 |
| prime radical | C61×#3176 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ #117×C61 ◁ C61×#405 ◁ G | |
544 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)(10,15)(11,19)(13,24)(14,23)(16,30)(17,33)(20,38)(21,39)(22,37)(25,26)(27,31)(28,35)(32,34)(36,40)(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)(9,10)(11,16)(12,15)(13,17)(14,18)(19,31)(20,27)(21,32)(22,28)(23,29)(24,35)(25,34)(26,36)(30,38)(33,37)(39,40);(9,11,12,20)(10,16,15,27)(13,25,22,39)(14,26,23,21)(17,34,28,40)(18,36,29,32)(19,37,38,24)(30,35,31,33);(1,3,4,7)(2,6,5,8)(10,15)(16,27)(17,28)(18,29)(30,31)(32,36)(33,35)(34,40)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26674);