Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7694 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C4 |
| direct product | C61×#7717 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C61 |
| Frattini, cosocle | C2×C42 | C23×C61 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C43×C61 ◁ G | |
352 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 3 generators on 101 points:
(1,2,4,6,5,3,7,8)(9,10)(11,17,19,14)(12,20)(13,16)(15,21)(18,22,24,23)(25,26)(27,33,35,40)(28,32)(29,31)(30,34,38,36)(37,39)(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);(1,3)(2,5)(4,6)(7,8)(9,11,13,19)(10,14,16,17)(12,18,21,24)(15,22,20,23)(25,27)(26,30)(28,36)(29,35)(31,38)(32,40)(33,39)(34,37);(2,3)(6,8)(9,12,13,21)(10,15,16,20)(11,18,19,24)(14,22,17,23)(26,31)(30,38)(32,39)(33,40)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 705);