Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C59 · Schur multiplier (H2) = C27 |
| direct product | C59×#34861 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C59 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C59 |
| socle | C23×C59 | C25 |
| prime radical | C59×#2388 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C59 ◁ G | |
2062 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 5 generators on 83 points:
(1,2)(3,6)(4,5)(7,8)(9,10)(11,14)(12,13)(15,16)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(2,5)(6,8)(17,18)(19,23)(20,22)(21,24);(10,13)(14,16)(17,19,20,24)(18,21,22,23);(9,11,12,15)(10,14,13,16)(18,22)(21,23);(1,3,4,7)(2,6,5,8)4484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 27849);