Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C61 · Schur multiplier (H2) = C28 |
| direct product | C61×#61692 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C61 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C61×#532 ◁ G | |
2078 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 5 generators on 85 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,14)(12,19)(13,17)(15,18)(16,20)(21,23)(22,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(1,3)(2,5)(4,8)(6,7)(9,11)(10,14)(12,19)(13,18)(15,17)(16,22)(20,24)(21,23);(9,12,15,21)(10,16,18,24)(11,19,17,23)(13,20,14,22);(3,8)(5,7)(9,10)(11,13)(12,16)(14,17)(15,18)(19,20)(21,24)(22,23);(2,6)(5,7)(9,13,15,14)(10,17,18,11)(12,20,21,22)(16,23,24,19)2989 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 54680);