Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#13305 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C59 |
| prime radical | C2×C59×#466 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C23×C4×C59 ◁ C23×C8×C59 ◁ G | |
618 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 3 generators on 83 points:
(1,2)(3,4)(9,10,13,17)(11,14,20,23)(12,21,19,16)(15,24,22,18)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(5,6)(7,8)(10,14)(11,18)(12,19)(15,16)(17,23)(20,24)(21,22);(2,4)(6,8)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 6293);