Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#33619 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C59 | C2×#466 |
| commutator, Frattini, cosocle | C2×C8 | C24×C59 |
| prime radical | C59×#3067 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C22×C4×C59 ◁ C2×#131×C59 ◁ G | |
636 conjugacy classes of subgroups.
| minimal degree | μ(G) = 123 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 123 points:
(1,2,8,14)(3,15,18,41)(4,22,25,39)(5,26,28,37)(6,13,7,12)(9,30,32,19)(10,29,36,24)(11,27,38,16)(17,46,47,63)(20,43,21,42)(23,54,55,35)(31,58,59,64)(33,50,34,44)(40,51,62,49)(45,53,56,61)(48,52,57,60)(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);(1,3,16,44,7,21,28,30,8,18,27,50,6,20,5,19)(2,9,26,43,13,34,38,41,14,32,37,42,12,33,11,15)(4,17,45,64,24,49,55,57,25,47,56,58,29,51,23,48)(10,31,53,46,22,52,54,62,36,59,61,63,39,60,35,40);(1,4)(2,10)(3,17)(5,23)(6,29)(7,24)(8,25)(9,31)(11,35)(12,39)(13,22)(14,36)(15,40)(16,45)(18,47)(19,48)(20,51)(21,49)(26,53)(27,56)(28,55)(30,57)(32,59)(33,60)(34,52)(37,61)(38,54)(41,62)(42,63)(43,46)(44,64)(50,58);(3,18)(9,32)(15,41)(17,47)(19,30)(20,21)(31,59)(33,34)(40,62)(42,43)(44,50)(46,63)(48,57)(49,51)(52,60)(58,64)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26607);