Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11234 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#11235 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | #391 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| socle | C2×C59 | #1441 |
| prime radical | C24×C59 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C23×C4×C59 ◁ G | |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2,6,10,7,12,5,11)(3,13,16,23,17,27,15,8)(4,18,19,26,20,25,21,9)(14,24,29,28,31,22,30,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3,5,15,7,17,6,16)(2,8,10,13,12,23,11,27)(4,14,19,29,20,31,21,30)(9,24,25,32,26,22,18,28);(1,4,5,19,7,20,6,21)(2,9,10,25,12,26,11,18)(3,14,15,29,17,31,16,30)(8,22,13,28,23,24,27,32)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4223);