Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#18522 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C59 |
| socle | C22×C59 | C2×#120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C2×C42×C59 ◁ G | |
1000 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 83 points:
(2,6)(3,4)(7,8)(9,10)(11,20)(12,23)(13,17)(14,18)(15,19)(16,22)(21,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(1,2,5,7)(3,6,4,8)(9,11,15,12)(10,16,19,24)(13,21,14,22)(17,20,18,23);(1,3,5,4)(2,6,7,8)(9,12,15,11)(10,16,19,24)(13,22,14,21)(17,20,18,23);(9,13,15,14)(10,17,19,18)(11,21,12,22)(16,20,24,23)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 11510);