Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C25 |
| direct product | C61×#18411 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C23×C61 | C22×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
870 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,6,10)(3,11,14,15)(4,9,5,8)(7,12,16,13)(18,22)(20,27)(23,31)(24,28)(25,29)(30,32)(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);(1,3,6,14)(2,7,10,16)(4,13,5,12)(8,11,9,15)(17,18,21,24)(19,23,26,32)(20,28,27,22)(25,30,29,31);(17,19,21,26)(18,23,24,32)(20,29,27,25)(22,30,28,31);(1,4,6,5)(2,8,10,9)(3,12,14,13)(7,15,16,11)(18,24)(22,28)(23,32)(30,31)2623 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 11399);