Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C22×C42 |
| direct product | C59×#33255 |
| 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 ◁ C43×C59 ◁ G | |
902 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 4 generators on 87 points:
(2,4)(5,6)(7,10)(8,9)(11,12)(13,14,19,25)(15,22,27,28)(16,20,26,21)(17,24,18,23)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(6,9)(10,12)(13,15,18,26,19,27,17,16)(14,20,24,28,25,21,23,22);(1,2,3,4)(13,15,17,16,19,27,18,26)(14,21,23,28,25,20,24,22);(5,7,8,11)(6,10,9,12)(13,16,17,27,19,26,18,15)(14,22,23,21,25,28,24,20)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26243);