Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#22853 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C59 | C24 |
| commutator | C23 | C23×C4×C59 |
| Frattini, cosocle | C22×C4 | C24×C59 |
| socle | C23×C59 | C23×C4 |
| prime radical | C59×#2388 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C59 ◁ G | |
1164 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 83 points:
(2,4)(5,6)(7,8)(9,10,13,17,14,11,15,19)(12,16,21,23,20,18,22,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(1,2)(3,4)(9,11,13,19,14,10,15,17)(12,16,21,23,20,18,22,24);(6,8)(9,12)(10,16)(11,18)(13,21)(14,20)(15,22)(17,23)(19,24);(2,4)(10,11)(12,20)(17,19)(21,22)4484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 15841);