Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C24×C4 |
| direct product | C59×#21698 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C59 | C22×D4 |
| commutator | C2×C4 | C23×C4×C59 |
| Frattini, cosocle | C22×C4 | C24×C59 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C59×#376 ◁ G | |
1014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 4 generators on 99 points:
(2,4)(5,6,8,7)(9,10,14,18)(11,19,23,33)(12,16,24,30)(13,26,20,17)(15,27,29,22)(21,32,35,40)(25,37,34,31)(28,38,39,36)(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);(9,11,20,27,14,23,13,22)(10,15,26,33,18,29,17,19)(12,21,34,38,24,35,25,36)(16,28,37,40,30,39,31,32);(1,2,3,4)(9,12,14,24)(10,16,18,30)(11,21,23,35)(13,25,20,34)(15,28,29,39)(17,31,26,37)(19,32,33,40)(22,36,27,38);(5,7,8,6)(12,24)(16,30)(21,35)(25,34)(28,39)(31,37)(32,40)(36,38)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 14686);