Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#29462 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C61 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C24×C61 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C22×C42×C61 ◁ G | |
766 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2)(3,7)(4,5)(6,8)(9,10)(11,15)(12,14)(13,16)(17,18,20,23,21,24,29,32)(19,25,26,30,27,31,28,22)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(2,5)(6,7)(9,11)(10,13)(12,16)(14,15);(11,16)(13,15)(17,19,21,27)(18,22,24,30)(20,28,29,26)(23,31,32,25);(1,3,4,8)(2,6,5,7)(10,14)(13,15)3538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 22450);