Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C23 |
| direct product | C59×#29189 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C59 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C59×#376 ◁ G | |
598 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,7)(4,5)(6,8)(9,10,12,14)(11,13,15,16)(17,18,21,24)(19,26,28,23)(20,30,25,22)(27,32,31,29)(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);(2,5)(6,7)(9,11,12,15)(10,13,14,16)(17,19,21,28)(18,23,24,26)(20,31,25,27)(22,29,30,32);(11,15)(13,16)(17,20,22,18,21,25,30,24)(19,27,29,26,28,31,32,23);(1,3,4,8)(2,6,5,7)(18,24)(19,28)(20,25)(29,32)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 22177);