Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#22734 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C59 | C24 |
| commutator | C22 | C23×C8×C59 |
| Frattini, cosocle | C22×C4 | C24×C59 |
| socle, prime radical | C23×C59 | C23×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C59 ◁ G | |
876 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 4 generators on 79 points:
(2,4)(6,10)(11,12)(13,14,15,17,16,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79);(5,6,9,10)(7,11,8,12);(1,2,3,4)(5,7,9,8)(6,11,10,12);(5,8,9,7)(6,11,10,12)5900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 15722);