Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C59 · Schur multiplier (H2) = C28 |
| direct product | C59×#62020 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C59 |
| prime radical | C59×#3561 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C59×#529 ◁ G | |
1772 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 5 generators on 99 points:
(2,5)(3,7)(9,10,13,17)(11,19,21,15)(12,23,24,32)(14,27,26,18)(16,28,31,25)(20,35,36,40)(22,30,38,34)(29,37,33,39)(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)(12,20)(13,21)(14,22)(16,29)(17,19)(18,30)(23,40)(24,36)(25,37)(26,38)(27,34)(28,39)(31,33)(32,35);(9,12,13,24)(10,16,17,31)(11,20,21,36)(14,28,26,25)(15,29,19,33)(18,32,27,23)(22,39,38,37)(30,35,34,40);(2,5)(6,8)(11,21)(15,19)(20,36)(22,38)(29,33)(30,34)(35,40)(37,39);(1,3,4,7)(2,6,5,8)(10,17)(11,21)(16,31)(18,27)(20,36)(22,38)(23,32)(37,39)2891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 55008);