Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7734 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C59 · Schur multiplier (H2) = C22 |
| direct product | C59×#7794 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C59 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C59 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C2×C42×C59 ◁ G | |
394 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 3 generators on 91 points:
(2,5)(3,7)(6,8)(9,10)(11,13)(12,15)(14,16)(17,18,21,24)(19,22,26,29)(20,23,27,30)(25,31,32,28)(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);(1,2,4,6)(3,8,7,5)(17,19)(18,22)(20,25)(21,26)(23,28)(24,29)(27,32)(30,31);(10,13)(11,16)(14,15)(17,20,21,27)(18,23,24,30)(19,25,26,32)(22,28,29,31)2183 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 782);