Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C25 |
| direct product | C61×#11131 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | #392 |
| commutator | C22×C4 | C22×C4×C61 |
| Frattini, cosocle | C23×C4 | C23×C61 |
| socle | C2×C61 | #1439 |
| prime radical | C22×#41×C61 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C23×C4×C61 ◁ G | |
852 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2,6,10,7,12,5,11)(3,13,17,23,16,24,15,8)(4,9,19,27,20,28,21,26)(14,29,18,22,30,25,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3,5,15,7,16,6,17)(2,8,10,13,12,23,11,24)(4,18,19,30,20,31,21,14)(9,25,26,22,28,29,27,32);(1,4)(2,9)(3,14)(5,21)(6,19)(7,20)(8,22)(10,27)(11,26)(12,28)(13,25)(15,31)(16,30)(17,18)(23,32)(24,29)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 4119);