Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#11244 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #124 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| socle | C22×C59 | #400 |
| prime radical | C24×C59 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C23×C4×C59 ◁ G | |
670 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 3 generators on 79 points:
(2,3)(5,6,11,14,10,15,9,19)(7,16,18,13,17,20,8,12)(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);(1,2,4,3)(5,7,9,8,10,17,11,18)(6,12,14,16,15,13,19,20);(1,3,4,2)(5,8,9,17,10,18,11,7)(6,13,14,20,15,12,19,16)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4232);