Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#17526 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | C22×D4 |
| commutator | C2×C4 | C23×C4×C59 |
| Frattini, cosocle | C42 | C24×C59 |
| socle | C22×C59 | C22×C22⋊C4 |
| prime radical | C59×#3483 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C4×#41×C59 ◁ G | |
990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,9)(4,13)(5,10)(6,15)(7,11)(8,12)(14,16)(17,18,21,24,22,26,20,25)(19,27,29,23,30,31,28,32)(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);(1,3,7,4)(2,8,11,16)(5,12,6,14)(9,10,13,15)(17,19,22,30)(18,23,26,32)(20,28,21,29)(24,31,25,27);(1,4,7,3)(2,9,11,13)(5,12,6,14)(8,10,16,15)(17,20,22,21)(18,24,26,25)(19,28,30,29)(23,31,32,27);(1,5,7,6)(2,10,11,15)(3,12,4,14)(8,13,16,9)(17,20,22,21)(18,25,26,24)(19,28,30,29)(23,27,32,31)3422 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 10514);