Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17547 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#17725 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C59 |
| Frattini, cosocle | C42 | C24×C59 |
| prime radical | C2×#41×C59 | D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C4×#41×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:
(2,6)(4,11)(7,13)(8,12)(10,15)(14,16)(17,18,21,25,22,26,20,24)(19,27,28,23,30,31,29,32)(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);(1,2,5,8)(3,7,9,14)(4,12,11,6)(10,16,15,13)(17,19)(18,23)(20,28)(21,29)(22,30)(24,31)(25,27)(26,32);(1,3,5,9)(2,7,8,14)(4,10,11,15)(6,13,12,16)(17,20,22,21)(18,24,26,25)(19,28,30,29)(23,31,32,27);(3,9)(7,14)(10,15)(13,16)3599 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 10713);