Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#26653 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C59×#2002 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ G | |
832 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 83 points:
(1,2)(3,6)(4,5)(7,8)(9,10,14,16,15,19,13,18)(11,12,21,24,17,23,20,22)(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);(10,16)(11,20)(13,14)(17,21)(18,19)(22,24);(2,5)(6,8)(9,11)(10,12)(13,20)(14,21)(15,17)(16,24)(18,22)(19,23);(1,3,4,7)(2,6,5,8)(9,12,15,23)(10,17,19,11)(13,24,14,22)(16,21,18,20)2537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 19641);