Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19883 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#19934 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C61 |
| prime radical | C61×#3366 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C42×C61 ◁ G | |
610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,5,8)(3,9,10,16)(4,13,14,7)(6,11,15,12)(17,18,22,25)(19,23,21,29)(20,27,28,31)(24,30,32,26)(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)(2,6)(4,11)(5,10)(7,16)(8,15)(9,13)(12,14)(17,19,22,21)(18,23,25,29)(20,26,28,30)(24,31,32,27);(3,10)(6,15)(9,16)(11,12)(17,20,22,28)(18,24,25,32)(19,26,21,30)(23,31,29,27);(3,11)(4,14)(6,16)(7,13)(9,15)(10,12)2623 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 12922);