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×#26650 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C59×#535 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ G | |
782 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2)(3,6)(4,5)(7,8)(9,10,13,18,14,19,29,33)(11,20,23,31,24,36,28,15)(12,16,25,34,27,35,26,17)(21,37,38,40,39,32,22,30)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(9,11,14,24)(10,15,19,31)(12,22,27,38)(13,28,29,23)(16,32,35,37)(17,30,34,40)(18,36,33,20)(21,25,39,26);(2,5)(6,8)(9,12)(10,16)(11,21)(13,25)(14,27)(15,30)(17,33)(18,34)(19,35)(20,37)(22,28)(23,38)(24,39)(26,29)(31,40)(32,36);(1,3,4,7)(2,6,5,8)(9,12)(10,17)(11,22)(13,26)(14,27)(15,30)(16,33)(18,35)(19,34)(20,32)(21,28)(23,39)(24,38)(25,29)(31,40)(36,37)2537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 19638);