Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#12790 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C61 | #117 |
| commutator | C2×C4 | C22×C8×C61 |
| Frattini, cosocle | C22×C8 | C23×C61 |
| socle | C22×C61 | #432 |
| prime radical | C24×C61 | M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C61 ◁ C2×#97×C61 ◁ G | |
450 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 3 generators on 97 points:
(2,4)(5,6,9,15,10,14,24,29,11,13,23,28,8,21,22,34)(7,16,18,31,19,26,33,35,20,30,32,36,17,12,25,27)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(1,2,3,4)(5,7,8,17,11,20,10,19)(6,12,14,16,13,26,21,30)(9,18,22,25,23,32,24,33)(15,27,29,31,28,35,34,36);(6,13)(9,23)(12,26)(14,21)(16,30)(18,32)(22,24)(25,33)3904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 5778);