Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#29786 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C61 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C24×C61 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C2×#117×C61 ◁ G | |
754 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 89 points:
(6,9)(10,12)(13,14,18,22,17,21,26,28)(15,23,24,20,16,19,25,27)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(1,2)(3,4)(5,6,8,9)(7,10,11,12)(13,15,17,16)(14,19,21,23)(18,24,26,25)(20,22,27,28);(2,4)(5,7)(6,10)(8,11)(9,12)(13,16,17,15)(14,20,21,27)(18,24,26,25)(19,22,23,28);(7,11)(10,12)(14,21)(15,16)(22,28)(24,25)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 22774);