Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C59 · Schur multiplier (H2) = C28 |
| direct product | C59×#61622 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C59 |
| prime radical | C59×#3489 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C59×#525 ◁ G | |
2028 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 5 generators on 99 points:
(1,2)(3,7)(4,6)(5,8)(9,10,15,19)(11,16,22,32)(12,23,25,33)(13,18,14,27)(17,28,34,24)(20,35,38,40)(21,30,26,31)(29,36,39,37)(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)(9,11)(10,16)(12,20)(13,26)(14,21)(15,22)(17,29)(18,31)(19,32)(23,35)(24,37)(25,38)(27,30)(28,36)(33,40)(34,39);(9,12,15,25)(10,17,19,34)(11,20,22,38)(13,24,14,28)(16,29,32,39)(18,33,27,23)(21,36,26,37)(30,35,31,40);(3,8)(5,7);(2,6)(5,7)(9,13,15,14)(10,18,19,27)(11,21,22,26)(12,24,25,28)(16,30,32,31)(17,33,34,23)(20,36,38,37)(29,35,39,40)2891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 54610);