Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C59 · Schur multiplier (H2) = C28 |
| direct product | C59×#60879 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C59 |
| prime radical | C59×#535 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C4×#41×C59 ◁ G | |
1654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 5 generators on 107 points:
(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18)(19,23)(20,25)(21,24)(22,27)(26,33)(28,35)(29,34)(30,37)(31,39)(32,38)(36,43)(40,44)(41,46)(42,45)(47,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,3,5,11)(2,6,8,9)(4,12,13,10)(7,15,16,14)(17,19,22,30)(18,23,27,37)(20,28,31,41)(21,29,33,43)(24,34,26,36)(25,35,39,46)(32,42,44,48)(38,45,40,47);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(18,24)(21,33)(23,34)(25,38)(26,27)(29,43)(32,44)(35,45)(36,37)(39,40)(42,48)(46,47);(2,8)(6,9)(7,16)(14,15)(17,20)(18,25)(19,28)(21,32)(22,31)(23,35)(24,38)(26,40)(27,39)(29,42)(30,41)(33,44)(34,45)(36,47)(37,46)(43,48);(20,31)(25,39)(28,41)(32,44)(35,46)(38,40)(42,48)(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, 53867);