Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23391 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C26 |
| direct product | C59×#23506 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C23×D4×C59 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C22×C42×C59 ◁ G | |
1574 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)(3,4)(6,7)(9,10,14,18)(11,19,21,23)(12,17,13,16)(15,20,24,22)(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);(5,6)(7,8)(11,20)(12,13)(15,23)(16,17)(19,24)(21,22);(2,4)(5,7,8,6)(9,11)(10,15)(12,20)(13,22)(14,21)(16,23)(17,19)(18,24);(11,21)(15,24)(19,23)(20,22)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 16494);