Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#11090 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | #393 |
| commutator | C24 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| socle | C2×C59 | #1439 |
| prime radical | C22×#41×C59 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C23×C4×C59 ◁ G | |
852 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2,5,10,6,9,19,24)(3,7,13,22,12,21,28,31)(4,14,17,25,16,8,18,23)(11,26,27,32,15,20,29,30)(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)(2,7)(4,15,16,11)(5,13)(6,12)(8,20,14,26)(9,21)(10,22)(17,29,18,27)(19,28)(23,30,25,32)(24,31);(1,4)(2,8)(3,11)(5,18)(6,16)(7,20)(9,14)(10,25)(12,15)(13,29)(17,19)(21,26)(22,32)(23,24)(27,28)(30,31)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4078);