Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C23×C4 |
| direct product | C61×#21295 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C61 | C22×D4 |
| commutator | C2×C4 | C23×C4×C61 |
| Frattini, cosocle | C22×C4 | C24×C61 |
| socle | C22×C61 | C2×C4×D4 |
| prime radical | C2×#135×C61 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C61 ◁ C2×#97×C61 ◁ G | |
722 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2)(3,6)(4,5)(7,8)(9,10,14,18,15,19,13,29)(11,16,23,32,21,31,22,38)(12,24,27,34,28,40,26,17)(20,35,37,33,25,39,36,30)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(2,5)(6,8)(9,11,14,23,15,21,13,22)(10,16,18,32,19,31,29,38)(12,25,27,36,28,20,26,37)(17,33,24,39,34,30,40,35);(9,12,13,26,15,28,14,27)(10,17,18,24,19,34,29,40)(11,20,22,36,21,25,23,37)(16,30,32,35,31,33,38,39);(1,3,4,7)(2,6,5,8)(11,21)(16,31)(20,25)(22,23)(30,33)(32,38)(35,39)(36,37)3904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 14283);