Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C59 · Schur multiplier (H2) = C26 |
| direct product | C59×#17351 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C22×C22⋊C4 |
| commutator | C22 | C23×C8×C59 |
| Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C22×#41×C59 | C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C4×D4×C59 ◁ G | |
1278 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 83 points:
(1,2,3,5,4,6,7,8)(9,10)(11,17,19,14)(12,15)(13,16)(18,23,24,21)(20,22)(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);(9,11,13,19)(10,14,16,17)(12,18,20,24)(15,21,22,23);(9,12)(10,15)(11,18)(13,20)(14,21)(16,22)(17,23)(19,24);(12,20)(15,22)(18,24)(21,23)4838 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 10339);