Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C61 · Schur multiplier (H2) = C28 |
| direct product | C61×#61666 |
| 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 | |
2064 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)(3,7)(4,6)(5,8)(9,10)(11,18)(12,25)(13,21)(14,20)(15,19)(16,24)(17,26)(22,36)(23,31)(27,35)(28,34)(29,33)(30,37)(32,39)(38,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,3)(2,5)(4,8)(6,7)(9,11,14,24)(10,16,20,18)(12,22,27,38)(13,28,15,23)(17,30,33,32)(19,34,21,31)(25,40,35,36)(26,39,29,37);(9,12,14,27)(10,17,20,33)(11,22,24,38)(13,26,15,29)(16,30,18,32)(19,25,21,35)(23,37,28,39)(31,36,34,40);(3,8)(5,7)(9,11)(10,18)(12,22)(13,28)(14,24)(15,23)(16,20)(17,32)(19,31)(21,34)(25,36)(26,39)(27,38)(29,37)(30,33)(35,40);(2,6)(5,7)(9,13,14,15)(10,19,20,21)(11,23,24,28)(12,26,27,29)(16,31,18,34)(17,25,33,35)(22,37,38,39)(30,36,32,40)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 54654);