Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3585 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C59 · Schur multiplier (H2) = C210 |
| direct product | C59×#60093 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | C23×D4 |
| commutator | C4 | C24×C4×C59 |
| Frattini, cosocle | C2×C4 | C25×C59 |
| socle | C2×C59 | C23×C22⋊C4 |
| prime radical | C2×C59×#585 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C22×#41×C59 ◁ G | |
4852 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 5 generators on 91 points:
(1,2,6,11,7,10,5,19)(3,12,14,8,15,23,20,22)(4,9,18,25,16,24,17,29)(13,26,28,21,27,32,30,31)(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)(2,8)(4,13)(5,20)(6,14)(7,15)(9,21)(10,22)(11,23)(12,19)(16,27)(17,30)(18,28)(24,31)(25,32)(26,29);(1,4)(2,9)(3,13)(5,17)(6,18)(7,16)(8,21)(10,24)(11,25)(12,26)(14,28)(15,27)(19,29)(20,30)(22,31)(23,32);(4,16)(9,24)(13,27)(17,18)(21,31)(25,29)(26,32)(28,30);(2,10)(8,22)(9,24)(11,19)(12,23)(21,31)(25,29)(26,32)4838 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 53081);