Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#27025 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C4×C4⋊C4×C61 ◁ G | |
642 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,5,8)(3,7,4,6)(9,10,12,14)(11,15,16,13)(17,18,20,23)(19,25,27,22)(21,24,28,31)(26,32,29,30)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3,5,4)(2,6,8,7)(9,11,12,16)(10,13,14,15)(19,26)(21,28)(22,30)(24,31)(25,32)(27,29);(10,14)(13,15)(17,19,20,27)(18,22,23,25)(21,29,28,26)(24,32,31,30);(1,4,5,3)(2,7,8,6)(10,14)(13,15)(19,27)(22,25)(26,29)(30,32)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 20013);