Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#22694 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | D42 |
| commutator | C2×C4 | C23×C4×C59 |
| Frattini, cosocle | C22×C4 | C24×C59 |
| socle | C2×C59 | D4×C4⋊C4 |
| prime radical | C2×#135×C59 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C22×C4×C59 ◁ G | |
812 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,7,12,8,13,6,25)(3,14,16,9,18,27,17,28)(4,19,15,29,21,26,20,10)(5,11,22,31,24,32,23,30)(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)(2,9)(4,5)(6,17)(7,16)(8,18)(10,11)(12,27)(13,28)(14,25)(15,22)(19,31)(20,23)(21,24)(26,30)(29,32);(1,4,6,20,8,21,7,15)(2,10,12,19,13,29,25,26)(3,5,17,23,18,24,16,22)(9,11,27,31,28,32,14,30);(1,5)(2,11)(3,15)(4,17)(6,23)(7,22)(8,24)(9,26)(10,27)(12,31)(13,32)(14,29)(16,21)(18,20)(19,28)(25,30)3422 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 15682);