Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#13383 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C61 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C61 |
| prime radical | C24×C61 | D8 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C23×C4×C61 ◁ C23×C8×C61 ◁ G | |
446 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 3 generators on 85 points:
(6,7)(9,10,11,14)(12,15,18,22)(13,21,19,17)(16,24,23,20)(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);(1,2)(3,4)(5,6)(7,8)(10,14)(15,22)(16,23)(17,21);(2,4)(5,7,8,6)(10,15)(12,20)(13,19)(14,22)(16,17)(18,24)(21,23)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 6371);