Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19186 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C23×C4 |
| direct product | C59×#19208 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C59 |
| prime radical | C23×C59 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G | |
606 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 91 points:
(2,6)(4,7)(8,12)(9,13)(11,14)(15,16)(17,18,21,24)(19,25,27,32)(20,28,30,23)(22,29,31,26)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,2,7,13,5,9,4,6)(3,8,14,16,10,15,11,12);(1,3)(2,8)(4,11)(5,10)(6,12)(7,14)(9,15)(13,16)(17,19,21,27)(18,22,24,31)(20,29,30,26)(23,32,28,25);(3,10)(8,15)(11,14)(12,16)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 12196);