Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#19155 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #121 |
| commutator, Frattini, cosocle | C42 | C24×C59 |
| socle | C22×C59 | C2×#121 |
| prime radical | C59×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C2×C42×C59 ◁ G | |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,10)(4,8)(5,14)(6,9)(7,13)(11,16)(12,15)(17,18)(19,25)(20,22)(21,29)(23,27)(24,28)(26,32)(30,31)(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);(1,3,5,13,6,11,4,12)(2,7,8,10,9,15,14,16)(18,22)(23,31)(24,29)(25,32);(3,11)(7,15)(10,16)(12,13)(17,19,20,26)(18,23,22,31)(21,30,28,27)(24,32,29,25);(1,4,6,5)(2,8,9,14)(3,12,11,13)(7,10,15,16)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 12143);