Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #29748 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C23×C4 |
| direct product | C61×#29860 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C2×AGL(1,ℤ/8)×C61 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
678 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2,4,5)(3,6,7,8)(9,10,15,20,13,18,14,19)(11,21,30,32,23,16,24,36)(12,25,29,17,27,35,28,34)(22,38,40,37,39,33,26,31)(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)(10,16)(12,26)(13,23)(14,24)(15,30)(17,33)(18,21)(19,32)(20,36)(22,29)(25,37)(27,40)(28,39)(31,35)(34,38);(3,7)(6,8)(9,12)(10,17)(11,22)(13,27)(14,29)(15,28)(16,31)(18,34)(19,35)(20,25)(21,37)(23,39)(24,40)(26,30)(32,38)(33,36);(1,3,4,7)(2,6,5,8)(12,27)(17,34)(22,39)(25,35)(26,40)(28,29)(31,37)(33,38)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 22848);