Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C61 · Schur multiplier (H2) = C25 |
| direct product | C2×C61×#1380 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C61 | D8 |
| commutator | C8 | C2×C42×C61 |
| Frattini, cosocle | C22×C8 | C23×C61 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C61 ◁ C23×C4×C61 ◁ C23×C8×C61 ◁ G | |
694 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 3 generators on 87 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(3,4)(5,6)(7,8,9,10)(12,17)(13,21)(14,23)(15,22)(18,19)(20,26)(24,25);(4,6)(11,12,14,18,15,19,13,17,16,20,21,25,22,24,23,26)5368 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 5543);