Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C26 |
| direct product | C61×#20669 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C61 | C22×D4 |
| commutator | C2×C4 | C23×C4×C61 |
| Frattini, cosocle | C22×C4 | C24×C61 |
| socle | C22×C61 | C22×C4⋊C4 |
| prime radical | C22×#41×C61 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C61 ◁ C22×#41×C61 ◁ G | |
1322 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 4 generators on 97 points:
(1,2)(3,4)(5,6,10,14,11,15,9,24)(7,16,20,26,18,30,19,12)(8,13,23,28,21,27,22,34)(17,29,32,35,33,36,31,25)(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);(5,7,9,19,11,18,10,20)(6,12,14,16,15,26,24,30)(8,17,22,31,21,33,23,32)(13,25,28,29,27,35,34,36);(2,4)(5,8)(6,13)(7,17)(9,22)(10,23)(11,21)(12,25)(14,28)(15,27)(16,29)(18,33)(19,31)(20,32)(24,34)(26,35)(30,36);(7,18)(8,21)(12,26)(13,27)(16,30)(19,20)(22,23)(28,34)3904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 13657);