Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C61 · Schur multiplier (H2) = C26 |
| direct product | C61×#10758 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C61 | #117 |
| commutator | C2×C4 | C2×C42×C61 |
| Frattini, cosocle | C23×C4 | C23×C61 |
| socle | C22×C61 | #381 |
| prime radical | C22×#41×C61 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C61 ◁ C2×#117×C61 ◁ G | |
1298 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 3 generators on 81 points:
(1,2)(3,4)(5,6)(7,14,16,11)(8,10)(9,13)(12,17)(15,19,20,18)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81);(6,10,13,12)(11,18,14,19);(2,4)(5,7)(6,11)(8,15)(9,16)(10,18)(12,19)(13,14)(17,20)3904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 3746);