Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C61 · Schur multiplier (H2) = C213 |
| direct product | C61×#62810 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C61 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C61 |
| socle | C22×C61 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C61 ◁ G | |
7220 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 6 generators on 85 points:
(1,2)(3,6)(4,5)(7,8)(9,10)(11,15)(12,19)(13,22)(14,17)(16,20)(18,24)(21,23)(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);(2,5)(6,8)(9,11,14,13)(10,15,17,22)(12,18,20,21)(16,23,19,24);(9,12)(10,16)(11,18)(13,21)(14,20)(15,23)(17,19)(22,24);(12,20)(16,19)(18,21)(23,24);(9,13,14,11)(10,15,17,22)(12,21,20,18)(16,23,19,24);(1,3,4,7)(2,6,5,8)5368 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 55798);