Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C59 · Schur multiplier (H2) = C23 |
| direct product | C59×#10198 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C59 |
| prime radical | C59×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G | |
508 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2,6,10)(3,11,13,16)(4,9,5,8)(7,14,15,12)(17,18,22,26)(19,27,30,31)(20,25,21,24)(23,29,32,28)(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);(1,3,6,13)(2,7,10,15)(4,14,5,12)(8,16,9,11)(17,19,22,30)(18,23,26,32)(20,29,21,28)(24,31,25,27);(1,3)(2,7)(4,12)(5,14)(6,13)(8,11)(9,16)(10,15)(19,28)(20,21)(23,27)(24,25)(29,30)(31,32)2183 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 3186);