Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33388 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C26 |
| direct product | C59×#33393 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C59 | C22×#102 |
| commutator | C8 | C23×C4×C59 |
| Frattini, cosocle | C2×C8 | C24×C59 |
| prime radical | C2×C59×#578 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C2×#41×C59 ◁ C2×#131×C59 ◁ G | |
1102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 123 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 123 points:
(1,2,6,11,7,13,27,12)(3,14,17,36,18,41,26,40)(4,9,21,34,19,32,48,35)(5,22,24,10,25,37,53,38)(8,23,29,16,31,45,30,46)(15,39,44,58,42,60,52,61)(20,49,51,33,47,59,64,57)(28,50,55,43,54,63,56,62)(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);(1,3,7,18)(2,8,13,31)(4,15,19,42)(5,23,25,45)(6,26,27,17)(9,28,32,54)(10,36,38,40)(11,30,12,29)(14,22,41,37)(16,24,46,53)(20,50,47,63)(21,52,48,44)(33,58,57,61)(34,56,35,55)(39,49,60,59)(43,51,62,64);(1,4)(2,9)(3,15)(5,20)(6,21)(7,19)(8,28)(10,33)(11,34)(12,35)(13,32)(14,39)(16,43)(17,44)(18,42)(22,49)(23,50)(24,51)(25,47)(26,52)(27,48)(29,55)(30,56)(31,54)(36,58)(37,59)(38,57)(40,61)(41,60)(45,63)(46,62)(53,64);(4,19)(9,32)(15,42)(20,47)(21,48)(28,54)(33,57)(34,35)(39,60)(43,62)(44,52)(49,59)(50,63)(51,64)(55,56)(58,61)3422 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26381);