Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C61 · Schur multiplier (H2) = C2 |
| direct product | C61×#7455 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C61 | D4 |
| commutator | C4 | C2×C32×C61 |
| Frattini, cosocle | C4×C16 | C22×C61 |
| socle, prime radical | C22×C61 | C4⋊C16 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C61 ◁ C4×C16×C61 ◁ G | |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 2 generators on 101 points:
(2,5)(3,7)(6,8)(9,10,11,15,12,16,19,25,13,17,20,26,22,28,31,35,14,18,21,27,23,29,32,36,24,30,33,37,34,38,39,40)(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);(1,2,3,5,4,6,7,8)6832 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 443);