Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C59 · Schur multiplier (H2) = C28 |
| direct product | C59×#62220 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C59 |
| prime radical | C59×#3518 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C59×#529 ◁ G | |
1640 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 5 generators on 107 points:
(1,2,5,8)(3,9,10,6)(4,12,13,7)(11,14,16,15)(17,18)(19,28)(20,33)(21,26)(22,27)(23,36)(24,31)(25,34)(29,44)(30,43)(32,39)(35,40)(37,41)(38,47)(42,45)(46,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,3)(2,6)(4,11)(5,10)(7,14)(8,9)(12,15)(13,16)(17,19)(18,24)(20,29)(21,30)(22,31)(23,32)(25,38)(26,39)(27,28)(33,48)(34,45)(35,46)(36,43)(37,47)(40,44)(41,42);(17,20,22,35)(18,25,27,41)(19,29,31,46)(21,34,23,37)(24,38,28,42)(26,40,36,33)(30,45,32,47)(39,44,43,48);(3,10)(6,9)(11,16)(14,15)(17,21,22,23)(18,26,27,36)(19,30,31,32)(20,34,35,37)(24,39,28,43)(25,40,41,33)(29,45,46,47)(38,44,42,48);(1,4,5,13)(2,7,8,12)(3,11,10,16)(6,14,9,15)(18,27)(19,31)(25,41)(26,36)(29,46)(30,32)(33,40)(45,47)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 55208);