Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C59 · Schur multiplier (H2) = C28 |
| direct product | C59×#62217 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C59 |
| prime radical | C59×#3515 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C59×#529 ◁ G | |
1642 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)(17,18,22,27)(19,28,31,24)(20,33,35,40)(21,26,23,36)(25,37,41,34)(29,44,46,48)(30,43,32,39)(38,45,42,47)(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)(17,19,22,31)(18,24,27,28)(20,29,35,46)(21,30,23,32)(25,38,41,42)(26,39,36,43)(33,48,40,44)(34,45,37,47);(17,20)(18,25)(19,29)(21,34)(22,35)(23,37)(24,38)(26,40)(27,41)(28,42)(30,45)(31,46)(32,47)(33,36)(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, 55205);