Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#25991 |
| 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 ◁ C4×C22⋊C4×C61 ◁ G | |
702 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)(4,6)(5,8)(9,10,12,14)(11,15,16,13)(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);(1,3,4,8)(2,5,6,7)(17,18)(19,26)(20,24)(21,29)(22,25)(23,27)(28,31)(30,32);(9,11,12,16)(10,13,14,15)(17,19,22,28)(18,23,25,32)(20,27,21,30)(24,31,29,26);(2,6)(5,7)(17,20,22,21)(18,24,25,29)(19,27,28,30)(23,31,32,26)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 18979);