Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C59 · Schur multiplier (H2) = C23×C4 |
| direct product | C59×#10893 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #120 |
| commutator | C2×C4 | C2×C42×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| socle | C22×C59 | #386 |
| prime radical | C24×C59 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C23×C4×C59 ◁ G | |
762 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 3 generators on 79 points:
(1,2,4,3)(5,6)(7,14)(8,17)(9,12)(10,13)(11,15)(16,20)(18,19)(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);(5,7,9,15,10,16,8,18)(6,11,12,20,13,19,17,14);(1,3,4,2)(5,6)(7,11)(8,17)(9,12)(10,13)(14,18)(15,20)(16,19)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 3881);