Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×#10594 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | #121 |
| commutator, Frattini, cosocle | C2×C42 | C23×C61 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C2×C42×C61 ◁ G | |
386 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 3 generators on 81 points:
(5,6,7,12,9,8,10,11)(13,14)(15,17)(16,19)(18,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81);(1,2)(3,4)(5,7,9,10)(6,11,8,12)(13,15,17,14,18,19,16,20);(2,4)(5,8,9,6)(7,12,10,11)(14,15)(16,17)(19,20)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 3582);