Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C27 |
| direct product | C59×#23399 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| socle | C22×C59 | C2×#120 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C23×C4×C59 ◁ G | |
2062 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 79 points:
(1,2)(3,4)(5,6)(7,12)(8,13)(9,17)(10,14)(11,15)(16,19)(18,20)(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);(5,7)(6,11)(8,15)(9,18)(10,16)(12,17)(13,19)(14,20);(2,4)(5,7)(6,12)(8,15)(9,18)(10,16)(11,13)(14,19)(17,20);(5,8,10,9)(6,13,14,17)(7,15,16,18)(11,19,20,12)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 16387);