Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#18067 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | C22×D4 |
| commutator | C2×C4 | C23×C4×C59 |
| Frattini, cosocle | C42 | C24×C59 |
| socle | C22×C59 | C2×C4×D4 |
| prime radical | C59×#532 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C4×M16×C59 ◁ G | |
654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 83 points:
(2,5)(3,7)(6,8)(9,10,14,17,13,16,22,24)(11,18,20,21,19,15,23,12)(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);(1,2,4,6)(3,8,7,5)(9,11)(10,15)(12,17)(13,19)(14,20)(16,18)(21,24)(22,23);(9,12,14,18,13,21,22,15)(10,11,17,20,16,19,24,23);(11,19)(12,21)(15,18)(20,23)4130 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 11055);