Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#18655 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C59 |
| prime radical | C2×#41×C59 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G | |
884 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,6,10)(3,11,14,15)(4,8,5,9)(7,13,16,12)(18,23)(19,27)(20,21)(25,26)(28,29)(30,31)(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)(2,7)(4,12)(5,13)(6,14)(8,15)(9,11)(10,16)(17,18,22,26)(19,24,28,32)(20,23,21,25)(27,30,29,31);(1,4,6,5)(2,8,10,9)(3,12,14,13)(7,15,16,11)(17,19,22,28)(18,24,26,32)(20,27,21,29)(23,30,25,31);(1,4,6,5)(2,9,10,8)(3,13,14,12)(7,15,16,11)(17,20,22,21)(18,25,26,23)(19,27,28,29)(24,31,32,30)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 11643);