Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24×C4 |
| direct product | C61×#29674 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C61 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C24×C61 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C2×#117×C61 ◁ G | |
1032 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 105 points:
(5,6)(7,10)(8,9)(11,12)(13,14,18,22)(15,19,24,33)(16,26,28,36)(17,29,31,21)(20,30,35,27)(23,37,38,44)(25,41,40,34)(32,42,43,39)(45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,2)(3,4)(6,9)(10,12)(13,15,18,24)(14,19,22,33)(16,23,28,38)(17,25,31,40)(20,32,35,43)(21,34,29,41)(26,37,36,44)(27,39,30,42);(2,4)(7,11)(10,12)(13,16,18,28)(14,20,22,35)(15,23,24,38)(17,30,31,27)(19,32,33,43)(21,36,29,26)(25,42,40,39)(34,44,41,37);(5,7,8,11)(6,10,9,12)(15,24)(19,33)(23,38)(25,40)(32,43)(34,41)(37,44)(39,42)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 22662);