Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#33900 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C59 |
| prime radical | C59×#3287 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C4×D4×C59 ◁ C8×D4×C59 ◁ G | |
558 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2,4,6)(3,7,8,5)(9,10,15,20)(11,21,22,38)(12,19,14,17)(13,26,29,34)(16,31,32,24)(18,25,36,28)(23,39,30,35)(27,37,40,33)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,3)(2,5)(4,8)(6,7)(11,22)(16,32)(21,38)(23,30)(24,31)(27,40)(33,37)(35,39);(9,11,15,22)(10,16,20,32)(12,23,14,30)(13,27,29,40)(17,33,19,37)(18,35,36,39)(21,34,38,26)(24,25,31,28);(3,8)(5,7)(9,12,15,14)(10,17,20,19)(11,23,22,30)(13,25,29,28)(16,33,32,37)(18,34,36,26)(21,35,38,39)(24,27,31,40)2537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26888);