Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8674 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×#8690 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #380 |
| commutator | C42 | C22×C4×C61 |
| Frattini, cosocle | C2×C42 | C23×C61 |
| prime radical | #121×C61 | Q8 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 3 generators on 101 points:
(1,2,4,7,5,3,8,6)(9,10)(11,20)(12,25,27,32)(13,28)(14,18)(15,19)(16,22)(17,26,33,29)(21,30,37,40)(23,31)(24,35)(34,36,39,38)(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);(9,11,13,22,15,24,14,23)(10,16,18,20,19,31,28,35)(12,21,26,36,27,37,29,38)(17,30,32,34,33,40,25,39);(1,3)(2,5)(4,6)(7,8)(9,12)(10,17)(11,21)(13,26)(14,29)(15,27)(16,30)(18,32)(19,33)(20,34)(22,36)(23,38)(24,37)(25,28)(31,40)(35,39)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1678);