Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#29525 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C61×#376 ◁ G | |
600 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,4,6)(3,7,8,5)(19,25)(20,28)(22,29)(24,30)(26,31)(27,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3,4,8)(2,5,6,7)(9,10)(11,14)(12,13)(15,16)(17,18)(19,26)(20,24)(21,23)(22,27)(25,31)(28,30)(29,32);(10,13)(14,16)(17,19,20,25,21,27,28,32)(18,22,24,29,23,26,30,31);(2,6)(5,7)(9,11,12,15)(10,14,13,16)(18,23)(22,26)(24,30)(29,31)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 22513);