Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33764 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#33824 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C59 |
| prime radical | C59×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ #117×C59 ◁ C59×#405 ◁ G | |
476 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 99 points:
(2,5)(3,7)(9,10,14,19)(11,15,20,28)(12,16,25,32)(13,26,24,18)(17,33,31,23)(21,27,34,38)(22,37,35,30)(29,40,39,36)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,2)(3,6)(4,5)(7,8)(9,11)(10,15)(12,21)(13,22)(14,20)(16,27)(17,29)(18,30)(19,28)(23,36)(24,35)(25,34)(26,37)(31,39)(32,38)(33,40);(2,5)(6,8)(10,16)(12,23)(13,24)(15,27)(17,18)(19,32)(21,36)(22,35)(25,33)(26,31)(28,38)(29,30)(34,40)(37,39);(1,3,4,7)(2,6,5,8)(11,20)(15,28)(21,34)(22,35)(27,38)(29,39)(30,37)(36,40)2360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26812);