Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#33874 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C59 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C4×D4×C59 ◁ C8×D4×C59 ◁ G | |
554 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,20)(12,17)(13,25)(14,29)(15,19)(16,23)(18,27)(21,36)(22,37)(24,35)(26,32)(28,39)(30,34)(31,38)(33,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,3)(2,5)(4,8)(6,7)(11,21)(16,31)(20,36)(22,30)(23,38)(26,40)(32,33)(34,37);(9,11)(10,16)(12,22)(13,26)(14,30)(15,21)(17,32)(18,34)(19,31)(20,25)(23,27)(24,38)(28,40)(29,33)(35,37)(36,39);(3,8)(5,7)(9,12,15,14)(10,17,19,29)(11,22,21,30)(13,24,28,27)(16,32,31,33)(18,25,35,39)(20,37,36,34)(23,26,38,40)2537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26862);