Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19713 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C23×C4 |
| direct product | C61×#19723 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C61 |
| prime radical | C61×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
678 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,7,11)(3,12,13,9)(4,8,14,16)(5,10,6,15)(19,25)(20,27)(22,28)(24,30)(26,31)(29,32)(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);(1,3,5,14,7,13,6,4)(2,8,15,9,11,16,10,12)(17,18)(19,22)(20,24)(21,23)(25,28)(26,29)(27,30)(31,32);(1,4,6,13,7,14,5,3)(2,9,10,8,11,12,15,16)(17,19,20,25,21,26,27,31)(18,22,24,28,23,29,30,32);(1,5,7,6)(2,10,11,15)(3,4,13,14)(8,9,16,12)(18,23)(22,29)(24,30)(28,32)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 12711);