Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8325 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C26 |
| direct product | C61×#10985 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #379 |
| commutator | C22×C4 | C22×C4×C61 |
| Frattini, cosocle | C23×C4 | C23×C61 |
| prime radical | C22×#41×C61 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G | |
1270 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 3 generators on 97 points:
(5,6)(7,15)(8,19,21,12)(9,22)(10,14)(11,17)(13,24)(16,30,32,29)(18,28)(20,27,36,34)(23,26)(25,31,33,35)(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);(1,2)(3,4)(5,7,10,18)(6,11,14,26)(8,16,21,32)(9,23,24,17)(12,25,19,33)(13,28,22,15)(20,35,36,31)(27,30,34,29);(2,4)(5,8)(6,12)(7,16)(9,20)(10,21)(11,25)(13,27)(14,19)(15,29)(17,31)(18,32)(22,34)(23,35)(24,36)(26,33)(28,30)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 3973);