Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C59 · Schur multiplier (H2) = C23×C4 |
| direct product | C59×#33421 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C59 | C24 |
| commutator | C22 | C23×C8×C59 |
| Frattini, cosocle | C2×C8 | C24×C59 |
| socle | C22×C59 | C23×C8 |
| prime radical | C2×#41×C59 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C59 ◁ G | |
582 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)(3,6)(4,5)(7,8)(9,10,12,17,13,18,22,30,14,16,23,28,24,29,34,38)(11,15,20,26,21,27,33,37,19,25,31,35,32,36,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(2,5)(6,8)(9,11)(10,15)(12,20)(13,21)(14,19)(16,25)(17,26)(18,27)(22,33)(23,31)(24,32)(28,35)(29,36)(30,37)(34,39)(38,40);(1,3,4,7)(2,6,5,8)(10,16)(15,25)(17,28)(18,29)(26,35)(27,36)(30,38)(37,40);(11,19)(15,25)(20,31)(21,32)(26,35)(27,36)(33,39)(37,40)5192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26409);