Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C59 · Schur multiplier (H2) = C28 |
| direct product | C59×#62240 |
| 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 | |
1632 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)(19,29)(20,34)(21,28)(22,27)(23,26)(24,32)(25,35)(30,44)(31,39)(33,40)(36,42)(37,41)(38,47)(43,45)(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)(20,30)(21,31)(22,32)(23,33)(25,38)(26,39)(27,29)(28,40)(34,48)(35,45)(36,46)(37,47)(41,43)(42,44);(17,20,22,36)(18,25,27,41)(19,30,32,46)(21,35,23,37)(24,38,29,43)(26,34,28,42)(31,45,33,47)(39,48,40,44);(3,10)(6,9)(11,16)(14,15)(17,21,22,23)(18,26,27,28)(19,31,32,33)(20,35,36,37)(24,39,29,40)(25,34,41,42)(30,45,46,47)(38,48,43,44);(1,4,5,13)(2,7,8,12)(3,11,10,16)(6,14,9,15)(18,27)(19,32)(25,41)(26,28)(30,46)(31,33)(34,42)(45,47)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 55228);