Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C26 |
| direct product | C61×#23980 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C61 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C22×D4×C61 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C2×C4×D4×C61 ◁ G | |
1222 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2)(3,4)(5,6)(7,11)(8,10)(9,12)(13,14,19,22)(15,17,21,18)(16,24,28,23)(20,27,25,26)(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);(5,7,8,12)(6,9,10,11)(13,15)(14,17)(16,25)(18,22)(19,21)(20,28)(23,27)(24,26);(2,4)(13,16,19,28)(14,20,22,25)(15,23,21,24)(17,27,18,26);(6,10)(9,11)(13,17,19,18)(14,21,22,15)(16,26,28,27)(20,23,25,24)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 16968);