Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24274 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#25135 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C59×#2407 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C2×C4×D4×C59 ◁ G | |
1124 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 83 points:
(1,2)(3,4)(9,10,13,19,15,20,14,18)(11,16,21,24,22,17,12,23)(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);(2,4)(5,6)(7,8)(9,11,13,21,15,22,14,12)(10,16,19,24,20,17,18,23);(6,8)(9,12,15,21)(10,17,20,16)(11,13,22,14)(18,23,19,24);(2,4)(9,13,15,14)(10,18,20,19)(11,12,22,21)(16,24,17,23)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 18123);