Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16×C61 · Schur multiplier (H2) = C23 |
| direct product | C2×C61×#1370 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C61 | D4 |
| commutator | C4 | C22×C16×C61 |
| Frattini, cosocle | C4×C8 | C23×C61 |
| socle, prime radical | C23×C61 | C4⋊C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C61 ◁ C2×C4×C8×C61 ◁ G | |
286 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 3 generators on 87 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(4,7)(5,8)(9,10)(11,12,13,16,14,17,19,22,15,18,20,23,21,24,25,26);(3,4,8,10,6,9,5,7)6832 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 4991);