Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9307 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C22×C4 |
| direct product | C59×#9309 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | #386 |
| commutator | C42 | C22×C4×C59 |
| Frattini, cosocle | C2×C42 | C23×C59 |
| prime radical | C59×#3036 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G | |
518 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 83 points:
(2,5)(3,6)(7,8)(9,10,13,16)(11,14)(12,15,20,17)(18,22)(19,23)(21,24)(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);(1,2,6,8,4,7,3,5)(9,11)(10,14,16,22)(12,19)(13,18)(15,23,17,21)(20,24);(2,7)(5,8)(10,15)(11,18)(12,20)(14,21)(16,17)(22,23)2183 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 2297);