Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C59 · Schur multiplier (H2) = C2×C4 |
| direct product | C59×#8227 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C59 | C2×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C59 |
| Frattini, cosocle | C2×C42 | C23×C59 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C43×C59 ◁ G | |
488 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 3 generators on 87 points:
(1,2,4,3)(5,6)(7,9)(8,11)(10,12)(13,14,16,19)(15,21,22,18)(17,25,24,20)(23,26,28,27)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(6,9,11,10)(13,15,17,23,16,22,24,28)(14,18,20,26,19,21,25,27);(1,3,4,2)(15,22)(18,21)(23,28)(26,27)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 1215);