Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#13072 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #466 |
| commutator | C2×C8 | C22×C4×C61 |
| Frattini, cosocle | C22×C8 | C23×C61 |
| prime radical | C2×#41×C61 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C2×#131×C61 ◁ G | |
458 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 3 generators on 97 points:
(1,2)(3,4)(5,6,10,15,12,8,11,22)(7,16,19,33,20,32,28,34)(9,23,25,21,27,36,26,14)(13,29,30,18,17,35,31,24)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(5,7,9,24,11,19,26,29,12,20,27,18,10,28,25,35)(6,13,21,16,15,31,36,34,8,17,14,32,22,30,23,33);(2,4)(5,8)(6,12)(7,17)(9,14)(10,15)(11,22)(13,20)(16,18)(19,30)(21,27)(23,26)(24,32)(25,36)(28,31)(29,33)(34,35)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 6060);