Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#10069 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C61 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C2×C42×C61 ◁ G | |
566 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 3 generators on 89 points:
(6,10)(7,8)(11,12)(13,14,18,22)(15,23,26,27)(16,19,17,21)(20,24,28,25)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(1,2)(3,4)(5,6,9,11)(7,10,8,12)(14,19)(16,17)(20,27)(21,22)(23,28)(24,25);(2,4)(5,7,9,8)(6,10,11,12)(13,15,18,26)(14,20,22,28)(16,25,17,24)(19,27,21,23)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 3057);