Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C59 · Schur multiplier (H2) = C28 |
| direct product | C59×#62023 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C59 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C59×#529 ◁ G | |
1792 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 5 generators on 99 points:
(2,5)(3,7)(9,10)(11,20)(12,24)(13,18)(14,19)(15,28)(16,23)(17,25)(21,36)(22,32)(26,33)(27,31)(29,34)(30,37)(35,39)(38,40)(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);(1,2)(3,6)(4,5)(7,8)(9,11)(10,16)(12,21)(13,27)(14,23)(15,22)(17,30)(18,32)(19,20)(24,40)(25,39)(26,38)(28,31)(29,37)(33,36)(34,35);(9,12)(10,17)(11,21)(13,25)(14,26)(15,29)(16,30)(18,33)(19,34)(20,35)(22,37)(23,38)(24,28)(27,39)(31,40)(32,36);(2,5)(6,8)(9,13,14,15)(10,18,19,28)(11,22,23,27)(12,25,26,29)(16,31,20,32)(17,33,34,24)(21,37,38,39)(30,40,35,36);(1,3,4,7)(2,6,5,8)(10,19)(11,23)(17,34)(18,28)(21,38)(22,27)(24,33)(37,39)2891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 55011);