Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#24767 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C2×C59×#469 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C2×#117×C59 ◁ G | |
1002 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 83 points:
(2,3)(9,10,14,16,12,17,13,18)(11,19,22,24,20,15,21,23)(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);(1,2,4,3)(5,6)(7,8)(9,11,12,20)(10,15,17,19)(13,21,14,22)(16,23,18,24);(6,8)(10,16)(13,14)(15,23)(17,18)(19,24)(21,22);(1,3,4,2)(10,17)(11,20)(16,18)(21,22)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 17755);