Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C59 · Schur multiplier (H2) = C23 |
| direct product | C59×#8066 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | C2×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C59 |
| Frattini, cosocle | C2×C42 | C23×C59 |
| socle | C22×C59 | C2×#95 |
| prime radical | C24×C59 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C22×C42×C59 ◁ G | |
542 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2,5,8,6,9,4,14)(3,10,13,15,11,16,12,7)(17,18)(19,26)(20,24)(21,30)(22,25)(23,28)(27,32)(29,31)(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)(2,7,9,15)(4,12)(5,13)(6,11)(8,10,14,16)(17,19,21,27,22,28,20,29)(18,23,24,32,25,26,30,31);(3,11)(7,15)(10,16)(12,13)(17,20,22,21)(18,24,25,30)(19,27,28,29)(23,31,26,32)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 1054);