Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#11188 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | #394 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| prime radical | C24×C59 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G | |
794 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 95 points:
(1,2)(3,4)(5,6,10,15,11,14,9,26)(7,16,19,32,20,12,18,28)(8,21,24,30,25,31,23,13)(17,29,22,27,35,36,34,33)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(5,7,11,20)(6,12,14,16)(8,22,25,34)(9,19,10,18)(13,29,30,36)(15,32,26,28)(17,23,35,24)(21,33,31,27);(2,4)(5,8)(6,13,14,30)(7,17)(9,23)(10,24)(11,25)(12,27,16,33)(15,21,26,31)(18,34)(19,22)(20,35)(28,36,32,29)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4176);