Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C59 · Schur multiplier (H2) = C210 |
| direct product | C59×#60089 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C23×D4 |
| commutator | C4 | C24×C4×C59 |
| Frattini, cosocle | C2×C4 | C25×C59 |
| prime radical | C2×C59×#585 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×#41×C59 ◁ G | |
4902 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 5 generators on 79 points:
(1,2,3,4)(6,11)(8,9)(12,18)(13,17)(15,16)(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)(7,12)(8,11)(9,17)(10,13)(14,19)(15,18)(16,20);(5,7)(6,12)(8,15)(9,16)(10,14)(11,18)(13,19)(17,20);(7,14)(12,19)(15,16)(18,20);(5,8,10,9)(6,11,13,17)(7,15,14,16)(12,18,19,20)4838 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 53077);