Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#18383 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C22×D4×C59 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G | |
986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,6,11)(3,13,17,29)(4,10,5,20)(7,12,23,30)(8,14,26,15)(9,19,21,22)(16,24,18,28)(25,31,27,32)(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);(1,3,6,17)(2,8,11,26)(4,15,5,14)(7,18,23,16)(9,28,21,24)(10,29,20,13)(12,27,30,25)(19,31,22,32);(1,2)(3,8)(4,9)(5,21)(6,11)(7,12)(10,22)(13,31)(14,24)(15,28)(16,25)(17,26)(18,27)(19,20)(23,30)(29,32);(1,4,6,5)(2,9,11,21)(3,14,17,15)(7,19,23,22)(8,24,26,28)(10,12,20,30)(13,27,29,25)(16,31,18,32)2537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 11371);