Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#18719 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C59 |
| prime radical | C59×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G | |
928 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)(6,8)(9,10,15,20)(11,21,24,34)(12,17,26,32)(13,19,14,18)(16,28,30,23)(22,35,38,39)(25,33,27,31)(29,36,40,37)(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);(3,7)(5,8)(9,11)(10,16)(12,22)(13,23)(14,28)(15,24)(17,29)(18,21)(19,34)(20,30)(25,36)(26,38)(27,37)(31,39)(32,40)(33,35);(1,2)(3,8)(4,6)(5,7)(9,12,15,26)(10,17,20,32)(11,22,24,38)(13,27,14,25)(16,29,30,40)(18,33,19,31)(21,35,34,39)(23,37,28,36);(9,13,15,14)(10,18,20,19)(11,23,24,28)(12,25,26,27)(16,21,30,34)(17,31,32,33)(22,36,38,37)(29,39,40,35)2360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 11707);