Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C61 · Schur multiplier (H2) = C28 |
| direct product | C61×#61286 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C61 |
| prime radical | C61×#532 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C61×#532 ◁ G | |
1754 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 5 generators on 101 points:
(1,2,5,4)(3,7,8,6)(9,10)(11,15)(12,17)(13,16)(14,18)(19,25)(20,27)(21,29)(22,26)(23,32)(24,30)(28,35)(31,36)(33,37)(34,38)(39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,3)(2,6)(4,7)(5,8)(9,11,14,21)(10,15,18,29)(12,20,23,34)(13,22,25,35)(16,26,19,28)(17,27,32,38)(24,33,36,40)(30,37,31,39);(1,4,5,2)(3,7,8,6)(10,16)(13,25)(15,26)(17,30)(18,19)(22,35)(24,36)(27,37)(28,29)(31,32)(33,40)(38,39);(3,8)(6,7)(9,12)(10,17)(11,20)(13,24)(14,23)(15,27)(16,30)(18,32)(19,31)(21,34)(22,33)(25,36)(26,37)(28,39)(29,38)(35,40);(10,18)(11,21)(12,23)(16,19)(22,35)(24,36)(27,38)(37,39)3538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 54274);