Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#10296 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C61 |
| prime radical | C23×C61 | #120 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
504 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2,6,10)(3,11,4,8)(5,14,15,9)(7,13,16,12)(17,18)(19,22)(20,23)(21,25)(24,29)(26,30)(27,32)(28,31)(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);(1,3,6,4)(2,7,10,16)(5,13,15,12)(8,14,11,9)(17,19,21,27)(18,22,25,32)(20,28,29,26)(23,31,24,30);(1,4,6,3)(2,8,10,11)(5,12,15,13)(7,9,16,14)(18,23)(20,29)(22,30)(24,25)(26,28)(31,32)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 3284);