Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#23601 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| socle | C22×C59 | C2×#121 |
| prime radical | C22×#41×C59 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C23×C4×C59 ◁ G | |
994 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 95 points:
(5,6,9,14,11,15,10,24)(7,16,18,27,20,33,19,12)(8,13,25,30,23,31,22,29)(17,32,35,26,34,28,21,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(1,2)(3,4)(5,7,10,19,11,20,9,18)(6,12,14,16,15,27,24,33)(8,21,22,34,23,35,25,17)(13,28,30,36,31,32,29,26);(2,4)(5,8)(6,13)(7,17)(9,22)(10,25)(11,23)(12,26)(14,29)(15,31)(16,32)(18,21)(19,35)(20,34)(24,30)(27,36)(28,33);(5,9,11,10)(6,14,15,24)(7,18,20,19)(8,22,23,25)(12,16,27,33)(13,29,31,30)(17,21,34,35)(26,32,36,28)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 16589);