Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#18802 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C59 |
| prime radical | C59×#3480 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G | |
958 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 83 points:
(2,6)(3,4)(7,8)(9,10,15,20)(11,21,23,17)(12,24,22,16)(13,19,14,18)(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)(3,6)(4,8)(5,7)(9,11)(10,16)(12,13)(14,22)(15,23)(17,18)(19,21)(20,24);(1,3,5,4)(2,6,7,8)(9,12,15,22)(10,17,20,21)(11,13,23,14)(16,18,24,19);(9,13,15,14)(10,18,20,19)(11,12,23,22)(16,17,24,21)2537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 11790);