Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C59 · Schur multiplier (H2) = C23 |
| direct product | C59×#13401 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | #482 |
| commutator, Frattini, cosocle | C22×C8 | C23×C59 |
| socle | C2×C59 | #2034 |
| prime radical | C59×#3067 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C22×C4×C59 ◁ C2×#131×C59 ◁ G | |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 123 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 123 points:
(1,2)(3,13)(4,19)(5,24)(6,28)(7,12)(8,15)(9,22)(10,27)(11,26)(14,42)(16,32)(17,33)(18,34)(20,53)(21,55)(23,52)(25,38)(29,37)(30,51)(31,47)(35,58)(36,57)(39,56)(40,44)(41,48)(43,64)(45,50)(46,59)(49,63)(54,61)(60,62)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123);(1,3)(2,8)(4,20)(5,17)(6,16)(7,18)(9,31)(10,34)(11,32)(12,33)(13,24)(14,23)(15,27)(19,50)(21,43)(22,54)(25,45)(26,48)(28,59)(29,60)(30,49)(35,40)(36,62)(37,61)(38,42)(39,63)(41,51)(44,57)(46,56)(47,58)(52,64)(53,55);(1,4,7,23)(2,9,12,36)(3,14)(5,25,27,21)(6,29,30,58)(8,31)(10,37,24,35)(11,38,39,55)(13,40)(15,45)(16,47)(17,43)(18,20)(19,51,52,28)(22,56,57,26)(32,42)(33,62)(34,61)(41,64)(44,48)(46,54)(49,60)(50,59)(53,63)2360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 6389);