Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C61 · Schur multiplier (H2) = C28 |
| direct product | C61×#60235 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C61 | C25 |
| commutator | C22 | C24×C4×C61 |
| Frattini, cosocle | C2×C4 | C25×C61 |
| socle | C22×C61 | C24×C4 |
| prime radical | C61×#3449 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C61 ◁ G | |
2094 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)(9,10,13,17,14,18,24,30)(11,15,21,27,20,26,33,37)(12,16,23,29,22,28,34,38)(19,25,32,36,31,35,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,3)(2,5)(4,8)(6,7)(9,11)(10,15)(12,19)(13,21)(14,20)(16,25)(17,27)(18,26)(22,31)(23,32)(24,33)(28,35)(29,36)(30,37)(34,39)(38,40);(3,8)(5,7)(9,12)(10,16)(11,19)(13,23)(14,22)(15,25)(17,29)(18,28)(20,31)(21,32)(24,34)(26,35)(27,36)(30,38)(33,39)(37,40);(2,6)(5,7)(12,22)(16,28)(19,31)(23,34)(25,35)(29,38)(32,39)(36,40);(11,20)(15,26)(19,31)(21,33)(25,35)(27,37)(32,39)(36,40)4636 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 53223);