Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#17836 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | C22×D4 |
| commutator | C2×C4 | C23×C4×C59 |
| Frattini, cosocle | C42 | C24×C59 |
| socle | C22×C59 | C22×C4⋊C4 |
| prime radical | C2×#41×C59 | Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C4×#41×C59 ◁ G | |
616 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 91 points:
(2,6)(4,7)(8,12)(9,13)(11,14)(15,16)(17,18,21,24,22,25,20,30)(19,26,28,31,29,32,27,23)(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);(1,2,7,13,5,9,4,6)(3,8,14,16,10,15,11,12)(17,19,21,28,22,29,20,27)(18,23,30,32,25,31,24,26);(1,3)(2,8)(4,11)(5,10)(6,12)(7,14)(9,15)(13,16);(3,10)(8,15)(11,14)(12,16)4130 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 10824);