Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12503 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C59 · Schur multiplier (H2) = C22×C8 |
| direct product | C59×#12515 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C59 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C42×C59 ◁ C82×C59 ◁ G | |
398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 3 generators on 83 points:
(2,5)(3,6)(7,8)(10,14)(11,15)(12,18)(16,24)(17,22)(19,23)(20,21)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(9,10,15,21,12,16,19,22,13,17,23,24,18,20,11,14);(1,2,6,8,4,7,3,5)4130 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 5503);