Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#23652 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | #397 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| socle | C2×C59 | C2×#397 |
| prime radical | C22×#41×C59 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C23×C4×C59 ◁ G | |
888 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,6,11,7,12,5,10)(3,13,15,8,17,24,16,25)(4,18,20,26,21,27,22,9)(14,29,31,32,19,23,30,28)(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)(2,8)(4,19)(5,15)(6,16)(7,17)(9,23)(10,24)(11,13)(12,25)(14,21)(18,32)(20,31)(22,30)(26,29)(27,28);(1,4,5,20,7,21,6,22)(2,9,10,18,12,26,11,27)(3,14,16,31,17,19,15,30)(8,23,13,28,25,29,24,32);(1,5,7,6)(2,10,12,11)(3,15,17,16)(4,20,21,22)(8,24,25,13)(9,18,26,27)(14,30,19,31)(23,32,29,28)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 16640);