Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19733 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C23×C4 |
| direct product | C61×#19741 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C61 |
| prime radical | C61×#3207 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
704 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 93 points:
(3,9)(4,11)(6,12)(8,14)(10,15)(13,16)(17,18,23,26)(19,27,31,28)(20,21,25,22)(24,29,32,30)(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);(1,2)(3,6)(4,8)(5,7)(9,12)(10,13)(11,14)(15,16)(17,19,21,29,23,31,22,30)(18,24,20,28,26,32,25,27);(1,3,4,9,5,10,11,15)(2,6,8,12,7,13,14,16)(17,20,22,18,23,25,21,26)(19,28,30,24,31,27,29,32);(2,7)(6,13)(8,14)(12,16)(17,21,23,22)(18,25,26,20)(19,29,31,30)(24,27,32,28)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 12729);