Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#33796 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C59 |
| prime radical | C23×C59 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ C2×C4×C8×C59 ◁ G | |
494 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)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18,20,25)(19,27,22,23)(21,24,29,32)(26,28,31,30)(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);(1,3,5,11)(2,6,8,9)(4,12,13,10)(7,15,16,14)(17,19,20,22)(18,23,25,27)(21,28,29,30)(24,26,32,31);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(18,24)(19,22)(21,30)(23,31)(25,32)(26,27)(28,29);(2,8)(6,9)(7,16)(14,15)(18,25)(23,27)(24,32)(26,31)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26784);