Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2069 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#11251 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | #396 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| socle | C2×C59 | #1441 |
| prime radical | C24×C59 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C23×C4×C59 ◁ G | |
620 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)(3,13)(4,18,21,26)(5,11)(6,10)(7,12)(8,15)(9,20,27,22)(14,30,32,23)(16,24)(17,28)(19,25,31,29)(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)(2,8,10,13,12,24,11,28)(4,19,20,14,21,31,22,32)(9,25,26,23,27,29,18,30);(1,4,5,20,7,21,6,22)(2,9,10,26,12,27,11,18)(3,14,15,31,17,32,16,19)(8,23,13,29,24,30,28,25)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4239);