Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#12894 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C61 | C23 |
| commutator | C22 | C22×C16×C61 |
| Frattini, cosocle | C22×C8 | C23×C61 |
| socle, prime radical | C23×C61 | C22×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C61 ◁ G | |
342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2)(3,8)(4,6)(5,7)(9,10)(11,13)(12,14)(15,16)(17,18,19,22,20,23,25,28,21,24,26,29,27,30,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3,5,4)(2,6,7,8)(9,11,12,15)(10,13,14,16);(1,4,5,3)(2,6,7,8)(10,14)(13,16)6832 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 5882);