Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18162 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#18172 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C59×#3492 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G | |
998 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,8,18)(3,12,23,32)(4,6,11,7)(5,17,24,28)(9,25,31,15)(10,21,20,22)(13,29,26,19)(14,27,16,30)(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);(1,3)(2,9)(4,13)(5,19)(6,16)(7,14)(8,23)(10,27)(11,26)(12,17)(15,22)(18,31)(20,30)(21,25)(24,29)(28,32);(1,4,7,2)(3,13,14,9)(5,20,22,28)(6,18,8,11)(10,21,17,24)(12,29,27,25)(15,32,19,30)(16,31,23,26);(3,14)(9,13)(12,27)(15,19)(16,23)(25,29)(26,31)(30,32)2360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 11160);