Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18682 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#18703 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C59 |
| prime radical | C23×C59 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G | |
812 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,10)(4,7)(5,9)(6,14)(8,12)(11,15)(13,16)(17,18,22,19)(20,27,28,32)(21,26,31,24)(23,30,25,29)(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)(4,11)(5,12)(6,15)(7,13)(9,16)(10,14)(17,19,22,18)(20,25,28,23)(21,24,31,26)(27,30,32,29);(1,4,7,2)(3,11,13,8)(5,9,6,14)(10,12,16,15)(17,20)(18,23)(19,25)(21,30)(22,28)(24,32)(26,27)(29,31);(1,5,7,6)(2,9,4,14)(3,12,13,15)(8,16,11,10)2360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 11691);