Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C59 · Schur multiplier (H2) = C28 |
| direct product | C59×#60339 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | C25 |
| commutator | C22 | C24×C4×C59 |
| Frattini, cosocle | C2×C4 | C25×C59 |
| socle | C22×C59 | C24×C4 |
| prime radical | C59×#537 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ G | |
1710 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 5 generators on 91 points:
(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18,20,23,21,24,27,30)(19,22,26,29,25,28,31,32)(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);(1,3,5,11)(2,6,8,9)(4,12,13,10)(7,15,16,14)(19,25)(22,28)(26,31)(29,32);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15);(2,8)(6,9)(7,16)(14,15);(17,19,20,26,21,25,27,31)(18,22,23,29,24,28,30,32)5192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 53327);