Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27×C61 · Schur multiplier (H2) = C221 |
| direct product | C25×D4×C61 |
| unambiguous semidirect product | C4⋊(C26×C61) |
| unambiguous semidirect product | C22⋊(C26×C61) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C26×C61 | C22 |
| commutator, Frattini, cosocle | C2 | C27×C61 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C26×C61 ◁ G | |
111198 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 7 generators on 75 points:
(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75);(3,4);(5,6);(7,8);(9,10);(1,2)(3,4)(5,6)(7,8)(9,10)(12,14);(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)9760 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 56083);