Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C61 · Schur multiplier (H2) = C24 |
| direct product | C2×C61×#1379 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C61 | D4 |
| commutator | C4 | C2×C4×C8×C61 |
| Frattini, cosocle | C22×C8 | C23×C61 |
| socle | C23×C61 | C22⋊C8 |
| prime radical | C24×C61 | M16 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C61 ◁ C23×C8×C61 ◁ G | |
606 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 3 generators on 99 points:
(1,2)(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);(7,8,11,16,12,17,26,34,13,18,27,35,10,15,24,32)(9,19,21,36,20,30,37,33,22,31,25,38,23,14,28,29);(3,4,5,6)(7,9)(8,14)(10,23)(11,25)(12,20)(13,22)(15,31)(16,33)(17,19)(18,30)(21,27)(24,37)(26,28)(29,35)(32,36)(34,38)6832 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 5541);