Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#13329 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C61 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C61 |
| prime radical | C22×D8×C61 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C2×C42×C61 ◁ C2×C4×C8×C61 ◁ G | |
578 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 3 generators on 101 points:
(1,2)(3,4)(9,10,14,19)(11,20,23,38)(12,16,27,34)(13,28,26,18)(15,30,32,21)(17,35,33,25)(22,39,29,36)(24,37,40,31)(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);(2,4)(5,6)(7,8)(9,11,14,23)(10,15,19,32)(12,24,27,40)(13,29,26,22)(16,20,34,38)(17,36,33,39)(18,37,28,31)(21,35,30,25);(6,8)(10,16)(12,25)(13,26)(15,20)(17,18)(19,34)(21,24)(22,29)(27,35)(28,33)(30,40)(31,39)(32,38)(36,37)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 6317);