Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C59 · Schur multiplier (H2) = C22 |
| direct product | C59×#13539 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C59 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C59 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C2×C42×C59 ◁ C2×C4×C8×C59 ◁ G | |
278 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2,5,7)(3,8,4,6)(9,10)(11,13)(12,14)(15,16)(17,18,20,22)(19,23,26,30)(21,24,28,29)(25,31,32,27)(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);(1,3,5,4)(2,6,7,8)(9,11,12,15)(10,13,14,16)(17,19,20,26)(18,23,22,30)(21,25,28,32)(24,31,29,27);(1,4,5,3)(2,6,7,8)(10,14)(13,16)(18,22)(19,25)(21,29)(23,27)(24,28)(26,32)(30,31)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 6527);