Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#33969 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C61 |
| prime radical | C2×D16×C61 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C4×Q8×C61 ◁ C8×Q8×C61 ◁ G | |
504 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 101 points:
(2,6)(7,8)(9,10,15,19)(11,20,21,37)(12,17,14,29)(13,25,28,39)(16,31,32,23)(18,24,36,27)(22,38,30,35)(26,33,40,34)(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);(1,2,5,6)(3,7,4,8)(11,21)(16,32)(20,37)(22,30)(23,31)(26,40)(33,34)(35,38);(1,3,5,4)(2,7,6,8)(9,11)(10,16)(12,22)(13,26)(14,30)(15,21)(17,33)(18,35)(19,32)(20,25)(23,27)(24,31)(28,40)(29,34)(36,38)(37,39);(1,4,5,3)(2,7,6,8)(9,12,15,14)(10,17,19,29)(11,22,21,30)(13,24,28,27)(16,33,32,34)(18,25,36,39)(20,38,37,35)(23,26,31,40)2623 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26957);