Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C59 · Schur multiplier (H2) = C22×C42 |
| direct product | C59×#10889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | #386 |
| commutator | C2×C4 | C2×C42×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| prime radical | C24×C59 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G | |
734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 79 points:
(1,2,4,3)(6,11)(8,9)(12,19)(13,14)(15,17)(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);(5,6,9,14,10,13,8,11)(7,12,15,19,16,20,17,18);(1,3,4,2)(5,7)(6,12)(8,17)(9,15)(10,16)(11,18)(13,20)(14,19)3422 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 3877);