Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#19375 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C61 |
| prime radical | C23×C61 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
554 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,6,10)(3,11,13,15)(4,14,7,8)(5,16,12,9)(17,18)(19,25)(20,28)(21,23)(22,26)(24,30)(27,32)(29,31)(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);(1,3,12,8,6,13,5,14)(2,7,16,15,10,4,9,11);(1,4)(2,8)(3,9)(5,15)(6,7)(10,14)(11,12)(13,16)(17,19,21,27)(18,22,23,31)(20,29,30,26)(24,32,28,25);(3,13)(4,7)(8,14)(11,15)(18,23)(22,31)(24,28)(25,32)2257 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 12363);