Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18316 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#18329 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C2×C59×#538 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G | |
1078 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)(3,13,16,22)(4,9,5,19)(7,12,17,10)(8,20,25,14)(15,29,30,28)(18,27,21,26)(23,31,24,32)(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)(2,8)(4,14)(5,20)(6,16)(7,15)(9,22)(10,23)(11,25)(12,24)(13,19)(17,30)(18,31)(21,32)(26,29)(27,28);(1,4,17,21)(2,9,10,26)(3,14,30,32)(5,7,18,6)(8,22,23,29)(11,19,12,27)(13,24,28,25)(15,31,16,20);(2,10)(8,23)(9,26)(11,12)(13,28)(19,27)(22,29)(24,25)2183 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 11317);