Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13331 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#13332 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C61 |
| prime radical | C2×C61×#509 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C2×C4×C8×C61 ◁ G | |
566 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 3 generators on 97 points:
(1,2)(3,4)(5,6)(7,17)(8,13)(9,15)(10,26)(11,16)(12,19)(14,23)(18,27)(20,32)(21,34)(22,33)(24,30)(25,31)(28,36)(29,35)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(2,4)(5,7,11,21)(6,12,16,29)(8,22,25,36)(9,18,10,20)(13,17,31,34)(14,32,30,27)(15,33,26,28)(19,24,35,23);(6,13)(7,18)(8,23)(9,10)(12,27)(14,15)(16,31)(17,33)(19,35)(20,21)(24,25)(26,30)(28,34)(29,32)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 6320);