Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#11932 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#102 |
| commutator | C2×C8 | C22×C4×C61 |
| Frattini, cosocle | C4×C8 | C23×C61 |
| prime radical | C23×C61 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ C2×C4×C8×C61 ◁ G | |
398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 3 generators on 101 points:
(1,2,3,6,4,5,7,8)(9,10)(11,20)(12,17)(13,26)(14,30)(15,19)(16,22)(18,28)(21,34)(23,40)(24,37)(25,35)(27,33)(29,36)(31,38)(32,39)(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);(2,5)(3,7)(9,11,15,24)(10,16,19,32)(12,23,14,21)(13,27,29,38)(17,33,30,31)(18,34,35,40)(20,36,37,26)(22,25,39,28);(9,12,15,14)(10,17,19,30)(11,21,24,23)(13,25,29,28)(16,31,32,33)(18,26,35,36)(20,34,37,40)(22,38,39,27)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 4920);