Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C61 · Schur multiplier (H2) = C28 |
| direct product | C61×#61216 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C61 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C61×#532 ◁ G | |
2060 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 5 generators on 101 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,16)(12,18)(13,20)(14,19)(15,21)(17,25)(22,30)(23,35)(24,32)(26,34)(27,31)(28,33)(29,37)(36,40)(38,39)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,3)(2,5)(4,8)(6,7)(9,11,15,24)(10,16,21,32)(12,22,26,38)(13,27,14,23)(17,29,33,40)(18,30,34,39)(19,35,20,31)(25,37,28,36);(9,12)(10,17)(11,22)(13,25)(14,28)(15,26)(16,29)(18,19)(20,34)(21,33)(23,36)(24,38)(27,37)(30,35)(31,39)(32,40);(3,8)(5,7)(9,12)(10,18)(11,22)(13,28)(14,25)(15,26)(16,30)(17,19)(20,33)(21,34)(23,37)(24,38)(27,36)(29,35)(31,40)(32,39);(9,13,15,14)(10,19,21,20)(11,23,24,27)(12,25,26,28)(16,31,32,35)(17,18,33,34)(22,36,38,37)(29,39,40,30)3538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 54204);