Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10690 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#10690 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #401 |
| commutator, Frattini, cosocle | C25 | C23×C61 |
| prime radical | C25×C61 | C23 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C25×C61 ◁ G | |
372 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2)(3,12,15,23)(4,16,31,25)(5,9)(6,11)(7,14,22,30)(8,18,26,19)(10,20)(13,27,28,24)(17,21,29,32)(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)(2,7,11,23)(4,17,18,28)(5,15)(6,14)(8,24,26,32)(9,22,10,12)(13,19,29,31)(16,27,25,21)(20,30);(1,4)(2,8,9,25)(3,13,14,28)(5,18)(6,19)(7,21,12,27)(10,26,11,16)(15,29,30,17)(20,31)(22,24,23,32)1525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 3678);