Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33657 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#33657 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C59 | C2×#481 |
| commutator, Frattini, cosocle | C2×C8 | C24×C59 |
| prime radical | C59×#3058 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C22×C4×C59 ◁ C2×#131×C59 ◁ G | |
566 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(3,11)(4,14)(5,17)(7,20)(9,24)(10,23)(12,28)(13,16)(15,30)(18,31)(19,29)(21,27)(22,25)(26,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,2)(3,7)(4,15)(5,10)(6,8)(9,18)(11,27)(12,21)(13,22)(14,30)(16,32)(17,23)(19,26)(20,28)(24,31)(25,29);(1,3,5,19,6,12,17,13)(2,7,10,26,8,21,23,22)(4,16,14,28,18,29,31,11)(9,25,24,27,15,32,30,20);(2,8)(7,21)(9,15)(10,23)(20,27)(22,26)(24,30)(25,32)2360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26645);