Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C23×C4 |
| direct product | C59×#21653 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C59 | C22×D4 |
| commutator | C2×C4 | C23×C4×C59 |
| Frattini, cosocle | C22×C4 | C24×C59 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C59×#376 ◁ G | |
770 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 4 generators on 87 points:
(1,2,4,3)(5,6)(7,10)(8,9)(11,12)(13,14,18,20)(15,21,23,22)(16,17,25,26)(19,27,28,24)(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)(10,12)(13,15,17,24,18,23,26,27)(14,19,16,21,20,28,25,22);(5,7,8,11)(6,10,9,12)(13,16,17,20,18,25,26,14)(15,22,24,19,23,21,27,28);(1,3,4,2)(15,23)(19,28)(21,22)(24,27)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 14641);