Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#33730 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C61 |
| prime radical | C23×C61 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ #117×C61 ◁ C61×#405 ◁ G | |
474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2,4,6)(3,7,8,5)(11,19)(12,23)(13,24)(15,26)(17,32)(18,31)(20,25)(21,36)(22,35)(27,30)(28,37)(29,40)(33,34)(38,39)(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);(1,3,4,8)(2,5,6,7)(9,10)(11,15)(12,17)(13,18)(14,16)(19,26)(20,27)(21,29)(22,28)(23,32)(24,31)(25,30)(33,38)(34,39)(35,37)(36,40);(9,11,20,36,13,21,12,19,14,22,23,34,24,33,25,35)(10,15,27,40,18,29,17,26,16,28,32,39,31,38,30,37);(10,16)(15,28)(17,30)(18,31)(26,37)(27,32)(29,38)(39,40)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26718);